Search

Reinforcement learning (RL) is a subfield of machine learning concerned with agents learning to behave optimally by interacting with an environment. One of the most important topics in RL is how the agent should explore, that is, how to choose actions in order to rate their impact on long-term reward. For example, a simple baseline strategy might be uniformly random action selection. This thesis investigates the heuristic idea that agents will learn faster if they explore by factoring the environment’s state into their decision and intentionally choose actions which are as different as possible from what they have previously observed. Experiments are run to discover whether this algorithm is computationally reasonable, and whether the agent learns significantly faster compared to baseline exploration strategies.

Forensic identification of source problems often fall under the category of verification problems, where recent advances in deep learning have been made by contrastive learning methods. Many forensic identification of source problems deal with a scarcity of data, an issue addressed by few-shot learning. In this work, we make specific what makes a neural network a contrastive network. We then consider the use of contrastive neural networks for few-shot learning classification problems and compare them to other statistical and deep learning methods. Our findings indicate similar performance between models trained by contrastive loss and models trained by cross-entropy loss. We also perform an ablation study to investigate the effects of different contrastive loss functions, metric functions, and margin values within contrastive learning. To test contrastive networks on real forensic data, we use the NBIDE cartridge casing dataset. Results are promising, as contrastive learning competed with older statistical methods while taking significantly less data preprocessing. Finally, we detail the desired invariance properties of embedding functions learned by contrastive networks in hopes that future work can enforce them through model architecture.

Optically stimulated luminescence (OSL) dosimetry was utilized to calibrate Al2O3:C powder dosimeters, available commercially as the nanoDot® from Landauer Inc., and compare the dosimeter response to radium-226 (226Ra) and cesium-137 (137Cs). The signal from the OSL was quantified using a microSTARii® OSL reader also produced by Landauer Inc. Dose-response curves were developed for 226Ra and 137Cs experiments (5 dosimeters each) at thirteen absorbed doses. Individual dosimeter response was tracked by serial number. Linear regression analysis was performed to determine if there were significant differences between the intercepts of the fit dose-response curves. A one-way analysis of variance (ANOVA) statistical test was used to determine the significance of the slope of the dose-response curve with follow-up analysis conducted to identify which dosimeter(s) has significantly different responses. The dosimeter response at 1mGy was determined to evaluate the manufacturer claim that accuracy (total uncertainty-single measurement) is ±10%. This study has illustrated that nanoDot dosimeters accuracy is generally within 10% of the actual absorbed dose over the dose range of 0.04 to 1.04 mGy, with a few of the measurements being different by 15%.

In the burgeoning field of quantum machine learning, the fusion of quantum computing and machine learning methodologies has sparked immense interest, particularly with the emergence of noisy intermediate-scale quantum (NISQ) devices. These devices hold the promise of achieving quantum advantage, but they grapple with limitations like constrained qubit counts, limited connectivity, operational noise, and a restricted set of operations. These challenges necessitate a strategic and deliberate approach to crafting effective quantum machine learning algorithms. This dissertation revolves around an exploration of these challenges, presenting innovative strategies that tailor quantum algorithms and processes to seamlessly integrate with commercial quantum platforms. A pivotal proposition within this framework is the creation of a resource-efficient quantum generative adversarial network (QGAN). This adaptation of QGANs, which are typically used to synthesize data according to specific probability distributions, ensures optimal performance even within environments with limited resources. Furthermore, our research delves deeply into the development of a data encoding procedure specifically designed for NISQ devices. This encoding process, responsible for translating classical data into quantum states to enable quantum algorithm processing, plays a critical role in quantum machine learning. Our goal is to establish an encoding approach that optimally utilizes quantum resources while mitigating the impact of noise and inherent limitations in NISQ devices. Another key aspect of our study is the seamless alignment of the devised algorithms with the existing architectures of NISQ devices. Given the pivotal role of these devices in contemporary quantum technology, ensuring compatibility is of utmost importance. This not only facilitates immediate applications but also establishes a robust framework for accommodating future technological advancements. Through an extensive analysis of these critical dimensions, our objective is to make a substantial contribution to the practical implementation of quantum machine learning algorithms on commercial quantum platforms. We aim to navigate the intricate landscape of NISQ technologies adeptly, thereby facilitating the seamless integration of quantum machine learning into real-world applications. Ultimately, this research endeavor aspires to drive advancements at the nexus of quantum computing and machine learning.

The gut microbiome plays a crucial role in human health, and by working collaboratively with microbiologists, we aim to further our understanding of the human gut and its impact on human health. Promoting a diverse microbiome is emphasized throughout microbiology literature, and involving a statistician in designing experiments to relate gut bacteria and some measured health outcome is crucial for ensuring valid and accurate results. By adopting new experimental design and analysis methods, researchers can begin to gain a deeper understanding of how the genetics of our food affect the composition of taxa within the gut microbiome. This dissertation is structured around three main objectives, demonstrating how applying new experimental design techniques and multivariate analysis methodologies could potentially benefit domain-specific researchers throughout the scientific process. This work developed a new experimental design structure for assigning treatments to well-plates. Multivariate analysis methods were used to analyze the data, creating new polymicrobial traits to introduce a community taxonomic effect into genome-wide association models. Finally, the effects of experimental parameters on statistical optimality criteria were explored. Our randomizations and experimental design structure exhibited increased efficiency over a design that included only replicate effects. After analyzing our taxonomic abundance data and decomposing the variability in multiple formats, our new pseudo-multivariate phenotypes were included in our collaborators' GWAS models. We found that 57\% of the calculated polymicrobial traits were included in the genome-wide association study (GWAS) models. Over half of the polymicrobial traits used as responses contained either a direct or related overlap with a univariate taxon on the same Major Effect Loci, where some of the unique and helpful relationships were explored more in-depth regarding taxonomic functions within the microbiome. Lastly, we developed a function that calculates the composite optimality criteria to compare design optimality for a multivariate linear mixed model with a covariance structure on the random genetic effects. In the future, similar models and optimal design functions could help researchers improve their experimental design layouts by leveraging their knowledge of genetic relationships in our diets and the relationships between taxa in the gut. Advisor: Kent Eskridge

In this dissertation, three primary issues are explored. The first subject exposes who-saw-from-whom pathways in post-specific dissemination networks in social media platforms. We describe a network-based approach for temporal, textual, and post-diffusion network inference. The conditional point process method discovers the most probable diffusion network. The tool is capable of meaningful analysis of hundreds of post shares. Inferred diffusion networks demonstrate disparities in information distribution between user groups (confirmed versus unverified, conservative versus liberal) and local communities (political, entrepreneurial, etc.). A promising approach for quantifying post-impact, we observe discrepancies in inferred networks that indicate the disproportionate amount of automated bots. Determine the most common organizational, political, and ideological dissemination pathways on Twitter. More misleading postings are followed by relatives and friends. The second theme is phylogenetics-related. In phylogenetics, likelihood techniques utilize a vast and diverse parameter space, which makes model selection more of a classification difficulty than an estimation one. We present a rooted triple approach for evolutionary tree inference that uses inter-taxon distances and k-fold cross-validation to assess if each triplet is tree-like. This new classification algorithm may be used to statistically infer level-1 networks. The final point pertains to temporal fairness. Customers in a service queue (such as a 311 call center) anticipate reasonable response times, particularly when there is no need to interrupt the first-come, first-served order. A temporally fair system delivers statistically equivalent service durations across sensitive population groups while permitting temporal fluctuations. We demonstrate that 311 service lines have treated demographic groups unevenly. We demonstrate that actual data are temporally unfair. Using our method, we slightly tweak the data in order to preserve statistical parity across groups and service times.

This dissertation is divided into two distinct parts. The main theme of the first part is to study stochastic processes (and related signal processing questions) using tools in wavelet analysis, functional analysis (we use in particular the trigonometric moment problem), the theory of realization of rational functions, and reproducing kernel Hilbert spaces. A novel form of multiresolution analysis is formulated in the discrete case that is used to study some stochastic processes. Using the trigonometric moment problem, we associate with a vector-valued wide-sense stationary process a multiresolution of a new kind. The notion of realization of rational functions was used to study stochastic processes and related signals. When the data is rational (meaning that the generating function of the covariance coefficients is rational) we used realization theory and the Kalman-Yakubovich-Popov (KYP) lemma to study this multiresolution. The idea of trigonometric moment problems in both the general and rational case were discussed. In the second part, we studied the trends of the average expenditure of diabetic patients over time. Four important breakdown costs were used to assess the total average expenditure of patients over time. The breakdown are average hospitalization cost, average management cost, average surgery cost, and average drug cost. The result indicated that the average hospitalization cost is higher among all the breakdowns for each year followed by the average management cost. The least average expenditure for each year is the average drug cost. The total average expenditure trend is expected to increase yearly. However, because of an intervention such as government policy that alleviates the cost of treatment, the average expenditure trend of patients changes sharply. We modeled the change in the total average expenditure using the piecewise linear regression model.

Evaluating association between variables is often of interest by many researchers. To serve this purpose, different association measures have been developed. However, type of relation between variables affects the degree of relationship. Hence, detection of the rela- tionship between variables is germane to measuring the correlation coefficient. With that mindset, here we explored six non-monotonic measure of association techniques and com- pared them with three classical approaches. Due to inconsistency in definition and range of different techniques, it is not feasible to compare the correlation estimates as their nature of variability differ. Therefore, we used permutation test based on Monte Carlo approximation for testing independence. We paired the correlation estimates along with the p-value for deciding strength of association between variables. At first, we explored and compared the association measures on twelve distinct simulation models under diverse scenario segregated by three sample sizes and three noise levels. In addition, we assessed the computational time and peak memory (RAM) usage during computations for each of these methods. Next, we applied all methods on Cape Floristic Region (CFR) data to capture association between four pairs of variable combinations with varying sample sizes. Overall, we found that, increasing sample size improves the performance of correlation measure. For any type of relationship, non-monotone measures were consistent in capturing association for large sample size. With respect to time and peak memory usage, we found two of the methods were not efficient.

This paper compares the predictive performance of two commonly used financial models, the Generalized Auto-Regressive Conditional Heteroskedasticity (GARCH) model, and the Stochastic Volatility model. Both techniques are used in the finance literature to model returns on an asset; the main difference between the two is that the former holds volatility as deterministic, whereas the latter treats it as a stochastic component. Three 10-year periods (2006-15, 2008-17, and 2010-19) of returns of the S&P-500 Index are used to train the two models. The parameter estimation is done using Hamiltonian Monte Carlo. Then, using Sequential Monte Carlo updates, returns for 2016, 2018, and 2020 are predicted, and their performance over different time frames—one month, one quarter, and one year—are compared using sum of squared errors (SSE). In addition, the percentage of observed returns for the three years that are captured between the 2.5 percentile and the 97.5 percentile of the predictions are compared. The results of the two models are practically indistinguishable by both criteria.

In this dissertation I will explore the question whether various entities commonly used in quantum field theory can be “constructed". In particular, can spacetime be “constructed" out of building blocks, and can Berezin integral be “constructed" in terms of Riemann integrals. As far as “constructing" spacetime out of building blocks, it has been attempted by multiple scientific communities and various models were proposed. But the common downfall is they break the principles of relativity. I will explore the ways of doing so in such a way that principles of relativity are respected. One of my approaches is to replace points with some entities that have a direction. In one of the sections, those entities are tangent vectors, in the other section they are pairs of points. In both cases, the success of respecting relativity is partial. On the one hand, I successfully removed preferred time axis. But, on the other hand, I still did not restore the symmetry under Lorentz group (or some modification of Lorentz group). For this reason, I also explored a different approach where I designed a matrix model for spacetime. In this case, I successfully restored Eucledian symmetry. Restoring the MInkowksian symmetry proved to be iii more difficult, and, depending on the models, came with the price. In both cases, though, the qestion of whether the resulting quantum field theory approximates the one that we know is left as an open question. There are reasons to hope that it does, but rigorously finding out whether that is the case is left for the future research. As far as constructing Berezin integral in terms of Riemann integrals, this was not attempted nearly as much (although there was one attempt in 1983 by Rabin, and possibly a couple of other isolated attempts). I have attempted to address it in my joint paper with Thomas Scanlon where we supplemented the anticommutting wedge product with Clifford algebra. This essentially amounts to “geometric algebra" model of Doran and Lasenby. Our contribution to that model is a design of specific sequence of integrals that would, in a limit, lead to Berezin integral. Finally, in the last chapter of the dissertation, I tie up those two projects by developing a graph-like interpretation of the Clifford structure that I used with Scanlon for Berezin integral. This implies that Berezin integral, itself, can also be modeled in terms of graphs. Those graphs are separate from the graphs used in the model of spacetime. A model of fermionic fields living in the spacetime would involve tensor products between those two types of graphs.

The U.S. Department of Education defines students with disabilities as those having a physical or mental impairment that substantially limits one or more life activities. Previous research has found that students with disabilities placed in inclusive environments perform better academically and socially compared to students with disabilities who are placed in segregated environments. Yet, we know that inclusion in K-12 general education classrooms across the country is not consistently implemented. The purpose of this study was to better understand the effects, if any, of general education high school teachers’ personal and professional experiences and knowledge on their attitudes toward educating students with disabilities within an inclusive learning environment. This study incorporated an explanatory sequential mixed methods approach. A survey was conducted with 173 teachers to gather quantitative data describing teachers’ attitudes, dispositions, and training, and then, in-depth interviews were conducted with a sub-sample of these teachers to better understand their preservice and inservice experience and knowledge about disability and inclusion. Findings of the study showed that prior experience with disability, along with training and support in best practices during preservice credential programs and inservice practice shaped teachers’ attitudes toward inclusion and in some cases hindered the implementation of inclusion models. The extent to which teachers had disability well defined in their preservice program, received training on regularly modifying assignments for students with disabilities, were provided a safe space in classes for disability to be discussed, and trained in how to implement positive behavior supports (PBS) in class, were more positively disposed toward inclusion. Conversely, a lack of an accountability system(s) seems to undermine the extent to which the K-12 school system is consistently implementing a model of inclusion and providing the necessary support for students with a disability. Overall, this study builds on our understanding of the issues that affect the implementation of inclusion and how best to support teachers in their efforts to support all students. This study has implications for those providing preservice to teachers and to school administrators who seek to support general education teachers’ disability inclusion efforts. Keywords: disability, attitudes about disability, inclusion, medical model of disability, social model of disability

The words people choose to use hold a lot of power, whether that be in spreading truth or deception. As listeners and readers, we do our best to understand how words are being used. There are many current methods in computer science literature attempting to embed words into numerical information for statistical analyses. Some of these embedding methods, such as Bag of Words, treat words as independent, while others, such as Word2Vec, attempt to gain information about the context of words. It is of interest to compare how well these various methods of translating text into numerical data work specifically with detecting fake news. The term “fake news” can be quite divisive, but we define it as news that is hyper-partisan, filled with untruths, and written to cause anger and outrage, as defined in Potthast & Kiesel (2018). We hypothesize a person’s word choice relates to the factualness of an article. In Chapter 5, we utilize this embedded information in several binary classification methods. We find that words are only marginally valuable in detecting fake news regardless of the embedding or classification method used. However, within natural language processing tasks, there are many preprocessing steps taken to get the text ready for analysis, which is explored in Chapter 6. The embedding methods are confounded with the preprocessing methods used. Preprocessing of text includes, but is not limited to, filtering out words that do not appear a minimum number of times, filtering out stop words, removing numbers, and translating all letters to lower case. We find filtering out stop words and removing words not appearing a minimum number of times have the most significant effect in combination with embedding and classification methods. Finally, in Chapter 7, we extend the classification to six categories ranging from true to pants-on-fire false and found these preprocessing methods are not as influential as they were with the binary outcome. Other predictors outside of the words and word embeddings themselves are necessary for improvement in the detection of fake news. Advisor: Kent Eskridge

Inverse problems involve extracting the internal structure of a physical system from noisy measurement data. In many fields, the Bayesian inference is used to address the ill-conditioned nature of the inverse problem by incorporating prior information through an initial distribution. In the nonparametric Bayesian framework, surrogate models such as Gaussian Processes or Deep Neural Networks are used as flexible and effective probabilistic modeling tools to overcome the high-dimensional curse and reduce computational costs. In practical systems and computer models, uncertainties can be addressed through parameter calibration, sensitivity analysis, and uncertainty quantification, leading to improved reliability and robustness of decision and control strategies based on simulation or prediction results. However, in the surrogate model, preventing overfitting and incorporating reasonable prior knowledge of embedded physics and models is a challenge. Suspended Nonstructural Systems (SNS) pose a significant challenge in the inverse problem. Research on their seismic performance and mechanical models, particularly in the inverse problem and uncertainty quantification, is still lacking. To address this, the author conducts full-scale shaking table dynamic experiments and monotonic & cyclic tests, and simulations of different types of SNS to investigate mechanical behaviors. To quantify the uncertainty of the inverse problem, the author proposes a new framework that adopts machine learning-based data and model driven stochastic Gaussian process model calibration to quantify the uncertainty via a new black box variational inference that accounts for geometric complexity measure, Minimum Description length (MDL), through Bayesian inference. It is validated in the SNS and yields optimal generalizability and computational scalability.

In this thesis, we focus on modeling categorical response variables from public opinion datasets. A hierarchical probit model was used to analyze these different variables. Particularly for multinomial data, we tried different covariate settings to see the model’s performance. For that purpose, we tried two different estimation techniques. The first algorithm uses identified parameters by fixing the first diagonal element of the covariance matrix at 1. The second algorithm uses one unidentifiable parameter and subsequently identifies the parameters by fixing the trace of the covariance matrix. The results from the simulation study confirm that the trace-restricted algorithm performs better with respect to convergence and mixing. However, the posterior probability prediction shows similar performance for both techniques. For real data analysis, we use opinions on the severity of “mental illness” and “HIV/AIDS” as our categorical responses; each of these has four categories. We classified these responses accordingly for binary, ordinal, and multinomial analysis. We evaluate the performance of our analysis using cross-validation and analytical tools.

Land use, such as logging and forest conversion to agriculture, can modify soil physicochemical and biological properties, and affect soil health. To understand how land use change can impact soil properties and canopy structure, we used a land use gradient in Malaysian Borneo consisting of six sites, including old growth forests, mixed forests, and agriculture fields. Specifically, we aimed to answer the following questions: (1) How do soil physicochemical properties vary across land use types? (2) Does bacterial diversity and composition vary across different land use types? (3) Does fungal diversity and composition vary across different land use types? We measured soil (top 5 cm) physicochemical properties (such as texture, temperature, water content, pH, organic matter, C and N content, and elements) and microbial properties (using next-generation amplicon sequencing). We also characterized understory and overstory canopy properties, including percent ground cover, canopy structure, and canopy closure. Our results indicate that old growth forests had the greatest forest cover and canopy closure, accumulated the highest soil organic matter, had a greater soil carbon and nitrogen ratio, were less acidic, and harbored greater bacterial and fungal diversity compared to mixed forests and agricultural fields. Old growth forests had a higher abundance of slow-growing specialist bacterial and fungal phyla, while agriculture fields had a greater abundance of rapidly growing opportunistic, generalist, and disturbance-resistant bacterial and fungal phyla. Our findings suggest that land use not only affects the aboveground surrounding forest cover and canopy closure, which has compounding effects with affected soil physical and chemical properties on soil microbial diversity, but also affects the microbial community composition and phylum function.

The electrophysiology of nodose ganglia neurons is of great interest in the analysis of cell membrane currents and action potential behavior. This behavior was initially outlined in the Hodgkin-Huxley conductance model [1] using a system of nonlinear differential equations. Later, Schild et al. [2] developed an extension of the Hodgkin-Huxley model to provide a more exhaustive description of ion channels involved in nodose neuronal action potential activity. We consider a variety of methods to fit the parameters of both the Hodgkin-Huxley and Schild et al. models to an empirical stimulus response dataset. Our methods were validated using synthetic datasets, as well as voltage-clamp data for nodose neurons. The fitting procedure that we implemented demonstrates the predictive efficacy of the Schild et al. model as well as its ability to provide a superior characterization of electrical signatures of nodose neurons.

Large neural networks have become ubiquitous in machine learning. Despite their widespread use, the optimization process for training a neural network remains com-putationally expensive and does not necessarily create networks that generalize well to unseen data. In addition, the difficulty of training increases as the size of the neural network grows. In this thesis, we introduce the novel MGDrop and SMGDrop algorithms which use a multigrid optimization scheme with a dropout coarsening operator to train neural networks. In contrast to other standard neural network training schemes, MGDrop explicitly utilizes information from smaller sub-networks which act as approximations of the full network. We empirically show that both MGDrop and SMGDrop perform comparably to existing training algorithms and in some cases are able to beat current algorithms in terms of accuracy and training time. In addition, we derive theoretical descriptions of the underlying update rules and their effects on network gradients.

For parallel-in-time integration methods, the multigrid-reduction-in-time (MGRIT) method has shown promising results in both improved convergence and increased computational speeds when solving evolution problems. However, one problem the MGRIT algorithm currently faces is it struggles solving hyperbolic problems efficiently. In particular, hyperbolic problems are generally solved using explicit methods and this causes issues on the coarser multigrid levels, where larger (coarser) time step sizes can violate the stability condition. In this thesis, physics-informed neural networks (PINNs) are used to evaluate the coarse grid equations in the MGRIT algorithm with the goal to improve convergence for problems with hyperbolic behavior, as well as improve stability for the time-stepping on coarser levels.

In this thesis, the basics of smoothing spline analysis of variance are first introduced. Regular physical activity has been shown to reduce the risk of chronic diseases in older adults, such as heart disease, stroke, diabetes, and certain forms of cancer. Accurate measurement of physical activity levels in older adults is crucial to identify those who may require interventions to increase their activity levels and prevent functional decline. In our study, we collected data on the physical activity of older individuals by utilizing accelerometer accelerometers. To estimate the underlying patterns related to each covariate, we applies smoothing spline analysis of variance (SSANOVA) methods to two types of measurements from the accelerometer device. We investigates the underlying patterns of different participant groups and compared the patterns among groups. The paper reveals clear patterns of activity levels throughout the day and across days, with differences among groups observed. Additionally, the study compares the mean curve method and the SSANOVA model, and shows that the SSANOVA model is a more suitable method for analyzing physical activity data. The study provides valuable insights into daily physical activity patterns in older people and highlights the usefulness of the SSANOVA model for such data analysis.

The quality control chart has long been used to monitor for a change in an industrial process. We discuss the Shewhart chart and CUSUM chart in their use for detecting a change in the process mean. We discuss the two sided CUSUM chart proposed by Uys and Lombard (2007). Integral equations are derived that are useful in analyzing the performance of the CUSUM charts. The performance of the Shewhart chart, the CUSUM chart, and the V-mask CUSUM chart in detecting a change point of the process mean are compared using simulation.

Handwriting analysis is a complex field largely living in forensic science and the legal realm. One task of a forensic document examiner (FDE) may be to determine the writer(s) of handwritten documents. Automated identification systems (AIS) were built to aid FDEs in their examinations. Part of the uses of these AIS (such as FISH[5] [7],WANDA [6], CEDAR-FOX [17], and FLASHID®2) are tomeasure features about a handwriting sample and to provide the user with a numeric value of the evidence. These systems use their own algorithms and definitions of features to quantify the writing and can be considered a black-box. The outputs of two AIS are used to compare to the results of a survey of FDE writership opinions. In this dissertation I will be focusing on the development of a response surface that characterizes the feature outputs of AIS outputs. Using a set of handwriting samples, a pairwise metric, or scoring method, is applied to each of the individual features provided by the AIS to produce sets of pairwise scores. The pairwise scores lead to a degenerate U-statistic. We use a generalized least squares method to test the null hypothesis that there is no relationship between two metrics (β1 = 0.) Monte Carlo simulations are developed and ran to ensure the results, considering the structure of the pairwisemetric, behave under the null hypothesis, and to ensure the modeling will catch a relationship under the alternative hypothesis. The outcome of the significance tests helps to determine which of the metrics are related to each other.

This thesis is an application of epidemiological models for infectious disease transmission and the use of partially observed Markov process (POMP) for model fitting. It focuses on COVID-19 pandemic in the state of New Mexico. The analysis covered March 2020 to June 2021. Daily data of COVID19 cases and deaths and a daily index of eleven statewide government non-pharmaceutical intervention (NPI) policies were collected from six public sources and were validated. These data were integrated through the Susceptible-Exposed-Infected-Removed (SEIR) model. Estimated daily transmission rates between the model compartments quantify the impact of the mitigation policies, and show that transmission rates and reproduction numbers decreased as policy index strengthened.

Large protected areas have long been the cornerstone of conservation biology, however, in an era branded by the human dominance of ecosystems, regional landscape structure and function are often a consequence of accumulated land-use decisions that may or may not include a nod to conservation planning. With underrepresentation of habitats in publicly protected areas, attention has focused on the function of alternative land conservation mechanisms. Private conservation easements (CEs) have proliferated in the United States, yet assessing landscape-level function is confounded by holder and donor intent, national and regional policy, regional landscape contexts, varying extents, resolution, and temporal scale. Over the last few decades, the use of conservation easements has proliferated and like other evolving concepts, it requires oversight and measurable evaluation in order to monitor and assess the usage and usefulness of the private conservation tool. To that point, this study explored the difference in composition and proximity tendencies of privately conserved lands relative to publicly conserved lands, and to random, private, non-conserved parcels using a remote measure of naturalness, first in chapter one as a pilot methodology in two Appalachian counties, and then in chapter two on a larger regional scale with more diverse geographic context. After gaining a better understanding of trends in composition and the link to the regional landscape, chapter three investigated tendencies in maintained and varying land cover composition across CE parcels and over time. Specifically, land cover composition was assessed from the time of placement using the NLCD 2019 land cover epochs, and compared to land cover in the epochs thereafter. This examination leveraged the National Conservation Easement Database (NCED) providing spatial and tabular data for CEs across the U.S. and allowing for diverse geographic contexts and landscape matrices. Variation in tests for differences, land characteristics, and human modification variables confirmed the significantly lower human modification of publicly protected lands, and opened the question as to the naturalness of easements in varying contexts. CEs in chapter one appeared to be representative of the mixed-use, rural-forested landscape rather than more natural land cover. Chapter two used the same methodology but expanded the geographic and landscape coverage resulting in a broader characterization of the composition of conservation easements, indicating that they were similar in naturalness to the landscape matrix to which they were located. Our findings when taken in light of other studies, suggested that conservation easements play variable roles in the extent that they conserve natural landscape condition and connectivity from county to county. Given this variable role, and that CEs are generally a random sample of their landscapes, chapter three explored the consistency with which CEs maintained the land cover composition in which they were originally placed. Approximately 70% of the parcels showed no change in land cover value for any of the points sampled, with nearly 94% of parcels showing no major change in dominant land cover within the parcel, across land cover epochs. These results indicate CEs are maintaining the dominant land cover they were placed in at least into the established NLCD epochs post-placement. Moreover, less than 1% of CE parcels showed a dominant land cover change into a developed land cover category, indicating that when there was change in dominant land cover, it typically was not into developed land covers. Given the substantial investment in privately conserved lands, these findings contribute to a better understanding of private conservation within various landscapes, and across varying conservation goals, development regimes, and circumstances of governance. The opportunity to use science as a guide by leveraging existing studies to build on prevailing conservation tools and strategies has the opportunity to actively progress through the “Conserving and Restoring America the Beautiful” initiative. The January 2021, U.S. President Biden recommended a collaborative and inclusive method to conserving America’s lands and waters for the benefit of all people. Specifically, the challenge encouraged pursuing conservation and restoration approaches that are flexible and adaptive and that support locally led and locally designed conservation efforts, honor private property rights, and support the voluntary stewardship efforts of private landowners. The initial report on the “America the Beautiful” issued in May 2021 indicated that conservation easements be an important part of its implementation, by their very definition and structure support the emphasis on locality, flexibility and adaptive approachs. Emerging research on the effectiveness of conservation easements in meeting conservation goals, including this study, provide a needed framework for implementing the “American the Beautiful” program.

Debiased Sinkhorn divergence (DS divergence) is a distance function of regularized optimal transport that measures the dissimilarity between two probability measures of optimal transport. This thesis analyzes the advantages of using DS divergence when compared to the more computationally expensive Wasserstein distance as well as the classical Euclidean norm. Specifically, theory and numerical experiments are used to show that Debiased Sinkhorn divergence has geometrically desirable properties such as maintained convexity after data normalization. Data normalization is often needed to calculate Sinkhorn divergence as well as Wasserstein distance, as these formulas only accept probability distributions as inputs and do not directly apply to signed data such as time signals and seismic waves; however, in doing so one may lose or distort information about the original signal. The investigations in this paper show that for high frequency signal inputs, Wasserstein distance may need a much more dramatic normalization compared to Debiased Sinkhorn in order to preserve convexity, leading to a loss of information about the original signal, the amplification of noise, and possibly machine overload, thus posing the desirability of the Debiased Sinkhorn divergence method.

Differential gene expression analysis has the potential to discover candidate biomarkers, therapeutic targets, and gene signatures. How to save money when using an unaffordable sample is a practical question. The case-cohort (CCH) study design can blend the economy of case-control studies with the advantages of cohort studies. But it has not been seen in the medical research literature where high-throughput genomic data were involved. A score test does not need to fit the Cox PH model iteratively; hence, it can save computing time and avoid potential convergence issues. We developed a score test under the CCH design to identify DEGs associated with survival outcomes. We provided asymptotic distribution theory and inferential procedures for the test. We also verified the validity of the inferential procedure in finite samples through simulation studies. When a permutation-based score test is used for survival outcome-related DEG analysis, the strong PH and probability distribution assumptions do not need to be a concern. However, it cannot be directly applied to the data from a CCH study design because a CCH sample is not a random sample. We developed a procedure to reconstruct a full cohort from a CCH sample and then perform the permutation-based score test on the reconstructed full cohort to identify the DEGs associated with survival outcomes. We evaluated our testing procedures and compared our methods with other existing approaches in terms of the FDR and the power through the simulation study and the application to the real datasets from two cancer-related genomic studies.

This thesis deals with Functional Data Analysis (FDA) on COVID data. The Data involves counts for new COVID cases, hospitalized COVID patients, and new COVID deaths. The data used is for all the states and regions in the United States. The data starts in March 1st, 2020 and goes through March 31st, 2021. The FDA smooths the data and looks to see if there are similarities or differences between the states and regions in the data. The data also shows which states and regions stand out from the others and which ones are similar. Also shown is which seasons are the best or worst for COVID-19. The data mainly focuses on finding if the regions and states are the same or different for new COVID cases, hospitalized COVID patients, and new COVID deaths.

In today’s world, deep learning models are widely used in a variety of fields. Audio applications include speech recognition, audio classification, and music information retrieval. In this paper, we will focus on the classification of music genres using an artificial neural network. The development of audio machine learning techniques has created an independence from traditional, more time-consuming signal processing techniques. Starting with raw audio data, we will gain an understanding of what audio is and its digital representation. Then, the focus will be on obtaining frequency information from audio signals through the use of spectrograms. Transforming the spectrograms into the perceptually relevant mel scale allows us to eventually extract mel frequency cepstral coefficients (MFCC) from audio files. We will then make use of our network architecture to process the MFCC’s. A convolutional neural network, our network of choice here, is trained to classify audio files into one of nine musical genres with an accuracy of 89.1% using the GTZAN dataset, which is only about 4 percentage points below the state-of-the-art performance for this dataset.

Log scales are often used to display data over several orders of magnitude within one graph. We conducted a series of three graphical studies to evaluate the impact displaying data on the log scale has on human perception of exponentially increasing trends compared to displaying data on the linear scale. Each study was related to a different graphical task, each requiring a different level of interaction and cognitive use of the data being presented. The first experiment evaluated whether our ability to perceptually notice differences in exponentially increasing trends is impacted by the choice of scale. Participants were shown a set of plots and asked to identify which plot appeared to differ most from the other plots. Results indicated the choice of scale changes the contextual appearance of the data leading to slight perceptual advantages for both scales depending on the curvatures of the trend lines being compared. The second study validated a new method, ‘You Draw It’, for testing statistical graphics and introduced an appropriate statistical analysis method for comparing visually fitted trend lines to statistical regression results. This new method was then used to test participant’s ability to make forecast predictions for exponentially increasing trends on both scales. The results from the analysis showed a clear underestimation of forecasting trends with high exponential growth rates when participants were asked to make predictions on the linear scale; improvement in forecasts were made when participants were asked to make predictions on the log scale. The third study evaluated graph comprehension as it relates to the contextual scenario of the data shown. Overall, our results suggested that log logic is difficult and that anchoring and rounding biases result in a sacrifice in accuracy in estimates made on the log scale for large magnitudes. The studies conducted in this research relied on graphical tasks of varying complexity to help us understand the perceptual and cognitive advantages and disadvantages of displaying exponentially increasing data on the log scale. The results are instrumental in establishing guidelines for making design choices about scale which result in data visualizations effective at communicating the intended results. Advisers: Susan VanderPlas and Reka Howard

This thesis derives two Uncertainty Quantification (UQ) methods for differential equations that depend on random parameters: (\textbf{i}) error bounds for a computed cumulative distribution function (\textbf{ii}) a multi-level Monte Carlo (MLMC) algorithm with adaptively refined meshes and accurately computed stopping-criteria. Both UQ approaches utilize adjoint-based \textit{a posteriori} error analysis in order to accurately estimate the error in samples of numerically approximated quantities of interest. The adaptive MLMC algorithm developed in this thesis relies on the adjoint-based error analysis to adaptively create meshes and accurately monitor a stopping criteria. This is in contrast to classical MLMC algorithms which employ either a hierarchy of uniform meshes or adaptively refined meshes based on Richardson extrapolation. Moreover, they also use a stopping criteria that relies on assumptions on the convergence rate of the MLMC levels. This thesis overcomes these drawbacks of the classical algorithms.The analysis and UQ methods developed in this these are applied to several types of differential equations and quantities of interest. Classical \emph{a posteriori} error analysis provides a formulation of the error in a Quantity of Interest (QoI) which is represented as a bounded linear functional of the solution to a differential equation. This thesis derives error estimates for a QoI that describes the \textit{time at which} a linear functional of the solution achieves a threshold value. This QoI is referred to as ``non-standard'' since it cannot be represented as a linear functional of the solution. The classical analysis does not directly apply to non-standard QoIs.The adjoint-based error analysis for the different QoIs not only develops accurate error estimates, they also provide a decomposition of the error into contributions from different regions of the domain. The decompositions are utilized to adaptively create meshes when adding new levels in the MLMC algorithm. Two adaptive mesh creation methods are described that can be used to build the MLMC estimator. Many numerical experiments demonstrate the accuracy of the error estimates and the advantages of using adaptive mesh creation in the MLMC algorithm.

This study compared the performance of machine learning models in classifying COVID-19 patients using exhaled breath signals and simulated datasets. Ground truth classification was determined by the gold standard Polymerase Chain Reaction (PCR) test results. A residual bootstrapped method generated the simulated datasets by fitting signal data to Autoregressive Moving Average (ARMA) models. Classification models included neural networks, k-nearest neighbors, naïve Bayes, random forest, and support vector machines. A Recursive Feature Elimination (RFE) study was performed to determine if reducing signal features would improve the classification models performance using Gini Importance scoring for the two classes. The top 25% of features determined by Gini Importance scores suggest that profiles from specific Volatile Organic Compounds (VOC) in patient breath may contribute to model performance.

In the first chapter of this dissertation we give a brief introduction to Markov chain Monte Carlo methods (MCMC) and their application in Bayesian inference. In particular, we discuss the Metropolis-Hastings and conjugate Gibbs algorithms and explore the computational underpinnings of these methods. The second chapter discusses how to incorporate spatial autocorrelation in linear a regression model with an emphasis on the computational framework for estimating the spatial correlation patterns. The third chapter starts with an overview of Gaussian mixture models (GMMs). However, because in the GMM framework the observations are assumed to be independent, GMMs are less effective when the mixture data exhibits spatial autocorrelation. To improve the performance of GMMs on spatially-correlated mixture data, chapter three describes a spatially correlated model that uses Gaussian process priors to account for the autocorrelation in the classifications. However, the inclusion of spatially correlated Gaussian processes results in a computational burden which is resolved by applying a P\`{o}lya-gamma data augmentation scheme that results in improved fit of the GMM in spatially correlated mixtures. Chapter three then compares the performance of the GMM and spatial GMM models on simulated data with and without spatial autocorrelation in the class labels. Both qualitative and quantitative model evaluation results support our assumption that the spatial GMM performs better when observation are spatially-autocorrelated. Chapter four applies the spatial Gaussian mixture model from chapter three to data obtained from ongoing work that aims to improve the accuracy in breast cancer margin assessment using THz imaging technology. In particular, the Bayesian estimate of uncertainty in the posterior probability from the spatial GMM shows promise in addressing the primary clinical question of determining the cancerous tumor margins.

Biologists are interested in estimating trait evolution models from phylogenies. However, phylogenies are imperfectly estimated, generally from DNA sequence data. In this study, true phylogenies are simulated to understand whether errors in phylogeny estimation affect inference of the trait evolution model. Given the tree, DNA sequences as well as traits are then simulated from the true phylogeny; both are simulated independently from the other. After the simulation, the DNA sequences were used to estimate trees using the UPGMA method without utilizing the trait information. The estimated trees combined with the traits are used to infer the evolutionary trait models, specifically the Brownian motion and the OU model. These results were also compared with estimating parameters of trait models from the true tree. Here we found the estimated evolutionary rates approach the true evolutionary rates as DNA sequence lengths and the number of taxa increase, but fluctuation occurs between different DNA sequence lengths greater than 500. Here, we found that estimates of trait evolution parameters were not very sensitive to errors in the gene tree when DNA sequences had length 500 or more.

Multilocus phylogenetic studies often show a high degree of gene tree heterogeneity —gene trees that have different topologies from each other as well as from the species tree topology. In some cases, this can lead to studies with hundreds of loci having distinct gene tree topologies. The degree of heterogeneity is expected to increase when there is a high degree of incomplete lineage sorting due to short branches (as measured in coalescent units) in the species tree. Other potential sources of heterogeneity include other biological processes such as introgression, recombination within genes, ancestral population structure, gene duplication and loss, and horizontal gene transfer, as well as gene tree estimation error due to short DNA sequences or inadequate substitution models. Here we examine the relationships between speciation and extinction rates and gene tree heterogeneity with both gene tree estimation error and no gene tree estimation error. In particular, higher speciation rates lead to shorter branches in the species tree and, therefore, higher levels of incomplete lineage sorting. In many cases, it might not be surprising that every gene tree has a unique topology, even for data sets with 1000 gene trees. We also propose using the average pairwise Robinson-Foulds (RF) distance between gene trees as a measure of heterogeneity as opposed to using the average RF distance between gene trees and the true species tree. Further, methods of inferring birth-death parameters (speciation and extinction rates) have involved using species trees estimated from gene trees or concatenation of DNA sequences. We infer these parameters using gene trees instead of species trees in this work. The method uses Approximate Bayesian Computation (ABC), which is useful when the maximum likelihood method is intractable, as in the case of gene trees given a species tree with a large number of taxa.

The piezoelectric response has been a measure of interest in density functional theory (DFT) for micro-electromechanical systems (MEMS) since the inception of MEMS technology. Piezoelectric-based MEMS devices find wide applications in automobiles, mobile phones, healthcare devices, and silicon chips for computers, to name a few. Piezoelectric properties of doped aluminum nitride (AlN) have been under investigation in materials science for piezoelectric thin films because of its wide range of device applicability. In this research using rigorous DFT calculations, high throughput ab-initio simulations for 23 AlN alloys are generated. This research is the first to report strong enhancements of piezoelectric properties in group IVB metals -- Titanium (Ti), Zirconium (Zr), and Hafnium (Hf) and partial enhancements in group VB metals -- Niobium (Nb) and Tantalum (Ta). Additionally, using a deep learning predictive model, predictions are made for optimal atomic compositions of solutes in AlN for sputter deposition. To demonstrate the use of machine learning (ML) algorithms in bioinformatics, the importance of features using an extreme gradient boosting algorithm is investigated for the derivation of the association between disease and genes. Moreover, a framework for better ML interpretability is also proposed.

Within recent decades, spectral methods have become an important technique in numerical computing for solving partial differential equations. This is due to their superior accuracy when compared to finite difference and finite element methods. For such spectral approximations, the convergence rate is solely dependent on the smoothness of the solution yielding the potential to achieve spectral accuracy. We present an iterative approach for solving the two-dimensional Helmholtz problem posed on a rectangular domain subject to Dirichlet boundary conditions that is well-conditioned, low in memory, and of sub-quadratic complexity. The proposed approach spectrally approximates the partial differential equation by means of modal Chebyshev integration matrices. Implementation of the boundary conditions is achieved through a technique known as ``integration preconditioning," although we refer to the technique as integration sparsification. The spectral method presented represents certain partial differential operators in terms of sparse, banded integration matrices. In this work, there are $N+1$ Chebyshev modes associated with each coordinate direction. Therefore, there are $n = (N + 1)^2$ modes in total. For the truncations considered, our method empirically yields a linear set-up cost, followed by a sub-quadratic solve complexity of $\mathcal{O}(n^{1.6})$.

Load forecasting is an important tool for both the energy and environmental sectors. It has progressed hand-in-hand with machine learning innovation, where recurrent neural networks, a type of artificial neural network, is primarily used. This thesis compares progressively complex, feed-forward artificial neural networks using a mix of weather and temporal data. We demonstrate that electrical load in New Jersey can be reliably predicted using memory-less algorithms with minimal predictors drawn from preexisting public data sources. The methods used in this thesis could be used to build competitive load forecasting models in other states, and if included in diverse model ensembles, may generate significant improvements.

The emergence of the novel coronavirus (SARS-CoV-2) in late 2019 has led to a global pandemic (COVID-19) which continues to cause enormous public health and economic challenges around the world. It is therefore important to improve our understanding of the outbreak and spread of COVID-19 as well as to investigate how one might contain or stop the spread of COVID-19 via different control measures. In this thesis, we consider a COVID-19 model based on an SEIR compartmental model. The model includes susceptible, vaccinated, exposed, pre-symptomatic, symptomatic infectious, asymptomatic infectious, hospitalized, recovered, and deceased compartments, each of which is sub-divided into 17 age groups. Furthermore, we incorporate contact structure which accounts for the number of contacts that individuals experience at school, work, home, and other environments. The model is parameterized based on New Jersey data, and we consider the effect of a hypothetical vaccine of varying efficacy that is introduced at the start of the epidemic outbreak in New Jersey. The results demonstrate how different control measures, including vaccine and lockdown, interact with each other and lead to different epidemic outcomes.

We consider an electrical parallel conductance membrane model which is an extension of the classical Hodgkin-Huxley neuronal model of excitability. This extended model describes the formation of the resting membrane potential and conductance, and the formation of action potentials in nodose A-type excitable cells. The model consists of a set of nonlinear ordinary differential equations which are numerically solved using the Python programming language. The results show that the model is capable of accurately describing experimental results including resting membrane potential and conductance, duration and form of action potentials, amplitude of the spike, oscillations, and activitydependent changes in [Ca2+] in the pericellular space and cytoplasm. This enables one to model the excitability of A-type nodose sensory neurons as well as to study the effects of ion channel modulators and their combinations under different environmental conditions such as variable extracellular Na+, K+, and Ca2+ concentrations and pericellular volume. The effects of tetrodotoxin which is found in pufferfish, 4-Aminopyridine chemical compound, and iberiotoxin which is found in the Indian Red Scorpion, were studied.

This dissertation includes two main topics. The first uses measurement error modeling to improve upon an existing method of inferring species trees from gene trees that were estimated with error. The second involves extending the parametric bootstrap (PB) approach, which was previously shown to work well for one- and two-way analysis of variance models with unequal variance and unbalanced data (heteANOVA), to multi-factor heteANOVA models. An overall framework using PB is presented. For each topic, the underlying theory is shown, and simulations and applications to empirical data are presented, demonstrating improvement over earlier methods. The proposed species tree inference method shows that species tree inference can be improved in the presence of gene tree estimation error, and the new method may be useful for inferring starting trees for other possibly slower methods. The PB methods developed here provide a viable alternative to transforming data to meet the equal variance assumption.

For 2 ≤ p < 4, we study the Lp norms of restrictions of eigenfunctions of the Laplace-Beltrami operator on smooth compact 2-dimensional Riemannian manifolds. Burq, G\´erard, and Tzvetkov [12], and Hu [21] found eigenfunction restriction estimates for a curve with nonvanishing geodesic curvatures. We will explain how the proof of the known estimates helps us to consider the case where the given smooth compact Riemannian manifold has nonpositive sectional curvatures. For p = 4, we will also obtain a logarithmic analogous estimate, by using arguments in Xi and Zhang [37], Sogge [33], and Bourgain [10]. At the end of this dissertation, we will talk about a future work, which is a follow up study for higher dimensional analogues of the above curve cases.

This study examined data from the United States Geological Survey Produced Water database, version 2.3 (USGS DB) and built models to estimate the concentration of radium-226 in produced water given the values of other predictor variables. The dataset had only about 254 observations that were useable. Although the USGS DB had up to 190 possible attributes, it also had extreme rates of missingness, and many of the candidate variables were highly correlated. Multiple imputation techniques were employed using the Mice, Hmisc, and RMS packages for the R language to deal with the missing data. A multiple linear regression and two logistic regression main effects models were fitted to the data. The bootstrap was used as a means of internal validation of models. The models concluded that log10(total dissolved solids) and log10(barium) appear to be significant predictors of log10(radium-226) and radium exceedance probabilities.

The muon’s anomalous magnetic moment, aμ, provides a unique way for probing physics beyond the standard model experimentally as it gathers contributions from all the known and unknown forces and particles in nature. The theoretical prediction of aμ has been in greater than 3 σ tension with the experimental measurement since the results of the Muon g-2 Experiment at the Brookhaven National Laboratory (E-821) were published in the early 2000s with a precision of 540 ppb. To settle this tension, the new Fermilab Muon g - 2 Experiment (E-989) is currently taking data with the aim of experimentally determining aμ with a final precision of 140 ppb. The determination of aμ involves measuring the magnetic field in which the muons undergo spin precession and the anomalous part of the spin precession frequency, ωa . We use a new reconstruction approach called the energy integrating method in which the total energy of the decay positrons deposited in the electromagnetic calorimeters is continuously recorded. This reconstruction method for the ωa analysis has different sensitivity to some of the major systematic biases compared to the traditional method which reconstructs individual positron events. Furthermore, we employ a ratio histogramming procedure that has reduced sensitivity to slow variations in the data. In this dissertation the muon g-2 experiment at Fermilab is described followed by a detailed discussion of the Run-2 and Run-3 precession frequency data analysis using the new energy integrating ratio histogramming method.

Radiogenomics is a new direction in cancer research that focuses on the associations among radiomics, genomics and clinical outcome. Currently, the major challenge for Radiogenomics lies in the effective integration of genomics and imaging data for promising clinical outcome prediction. Herein, we propose a multivariate joint model that can integrate imaging and genomic data for better predicting the clinical outcome. Specifically, we jointly consider two multivariate group lasso models, one regresses imaging features on genomic features, and the other regresses patient’s clinical outcome on genomic features. An L1 penalty term is introduced for each variable, and weight in the penalty term is considered to allow features to have a higher chance of selection by one model if they are selected by the other model. In addition, we include an L2 penalty term in the model since genomic pathway and imaging types are incorporated as group information to improve feature selection. Subsequently, we implement an accelarated generalized coordinate descent algorithm for the joint model. We first build the model for radiogenomics data with continuous outcome, and then extend the model and algorithm to data with survival outcome. Our joint model allows the use of separate datasets to fit the two models, resolving the existing limitations in available datasets. As there are many public datasets only has genomic but not imaging information, our approach enables to utilize such datasets in combination with other datasets where imaging data is available, thereby to better predict the clinical outcome. Simulations and real data analyses demonstrate that our methods outperform the existing methods in the literature. Finally, an R package rgjoint for the proposed methods is developed and presented in this dissertation.

In non-inferiority testing, the decision of whether a proposed treatment is non-inferior to a reference treatment depends on model assumptions and choices of acceptable tolerance limits. Here, we consider a method that employs kernels to estimate the probability density functions of both the experimental and reference populations from two independent samples. Based on these densities, we introduce a quantity called the overlap coefficient or overlap measure. A bootstrap technique is helpful in exploring the distribution and variance empirically. We derive the distribution of this measure and define a hypothesis test that can be applied to the non-inferiority setting under some simplifying assumptions about distributions of the populations.

As the population of the Earth increases, there is a growing need for food to feed the inhabitants. Precision agriculture offers techniques and tools that can be used to help accommodate the growing population. One specific precision agriculture tool is remote sensing data, which can be used to image fields as an effort to better predict or understand the crops. In this thesis, deep neural networks are used to evaluate various spatial, spectral, and temporal resolutions of three different satellite images to determine which best predicts corn yield. The main metrics we used to evaluate the models were R-squared (R2), root mean squared error (RMSE), and mean absolute error (MAE). Regarding spectral resolutions, our results suggest that more granularity produces better models. For spatial resolutions, our results suggest less granularity performs better. Additionally, our results found that high frequency temporal resolution does not produce perform better than low frequency temporal resolution.

Soybean is a significant source of protein and oil, and also widely used as animal feed. Thus, developing lines that are superior in terms of yield, protein and oil content is important to feed the ever-growing population. As opposed to the high-cost phenotyping, genotyping is both cost and time efficient for breeders while evaluating new lines in different environments (location-year combinations) can be costly. Several Genomic prediction (GP) methods have been developed to use the marker and environment data effectively to predict the yield or other relevant phenotypic traits of crops. Our study compares a conventional GP method (GBLUP), a kernel method (Gaussian kernel [GK]), a machine learning method (deep learning [DL]) and a hybrid method that corresponds to the emulation of a machine learning model using a kernel method (and arccosine kernel [AK]) in terms of their prediction accuracies for predicting grain yield, oil and protein using data from the Soybean Nested Association Mapping experiment (1,379 genotypes tested in six environments, all genotypes in all environments). The relative performance of the four methods varied with the response variable and whether the model includes the genotype-by-environmental interaction effects or not. GBLUP consistently showed better performances, while GK and AK followed a similar pattern to GBLUP, DL performed slightly worse than the other three methods in most of the cases; however, this may also be attributed to sub-optimal hyperparameters. DL performed particularly worse than the other three methods in presence of the genotype-by-environmental interaction effects. In general, all four methods performed better when the interaction effects were included compared to the main effects only models. Advisor: Reka Howard

Linear operators are of huge importance in modern harmonic analysis. Many operators can be dominated by finitely many sparse operators. The main result in this thesis is showing a toy operator, namely the Martingale Transform is dominated by a single sparse operator. Sparse operators are based on a sparse family which is simply a subset of a dyadic grid. We also show the A2 conjecture for the Martingale Transform which follows from the sparse domination of the Martingale Transform and the A2 conjecture for sparse operators. .

In 2016, the CareLink New Mexico behavioral health homes program began enrolling Medicaid recipients with the goal of increasing care coordination, improving access to services, and decreasing long-term costs of care for adults with serious mental illness (SMI) and children with severe emotional disturbance (SED). To evaluate these aims, a retrospective interrupted time series study using Medicaid claims data was designed. First, a comparable subset of non-enrolled individuals was selected from the pool of Medicaid recipients with SMI or SED using propensity score matching. Then, segmented regression was applied to three outcomes: total Medicaid charges, number of outpatient behavioral health claims, and incurring emergency care claims. Finally, difference-in-difference contrasts were estimated to compare the enrolled individuals’ outcomes to their own baseline and to the trajectory of non-enrolled individuals. Enrollment resulted in decreased rate of increase in costs, decreased behavioral health claims, and decreased probability of emergency health care for enrollees.

This paper will outline a Debiased Sinkhorn Divergence driven Bayesian inversion framework. Conventionally, a Gaussian Driven Bayesian framework is used when performing Bayesian inversion. A major issue with this Gaussian framework is that the Gaussian likelihood, driven by the L2 norm, is not affected by phase shift in a given signal. This issue has been addressed in [1] using a Wasserstein framework. However, the Wasserstein framework still has an issue because it assumes statistical independence when multidimensional signals are analyzed. This assumption of statistical independence cannot always be made when analyzing signals where multiple detectors are recording one event, say from a seismic event. The Wasserstein metric can be generalized to multidimensional signals, but implementation of the multidimensional Wasserstein metric is very computationally expensive. This means that it is unreasonable for Bayesian inversion. Debiased Sinkhorn Divergence offers an alternative to the multidimensional Wasserstein metric while remaining relatively cheap computationally. This allows for the creation of a Debiased Sinkhorn Divergence driven Bayesian framework that will be formulated and analyzed in this paper.

Data reconstruction is significantly improved in terms of speed and accuracy by reliable data encoding fragment classification. To date, work on this problem has been successful with file structures of low entropy that contain sparse data, such as large tables or logs. Classifying compressed, encrypted, and random data that exhibit high entropy is an inherently difficult problem that requires more advanced classification approaches. We explore the ability of convolutional neural networks and word embeddings to classify deflate data encoding of high entropy file fragments after establishing ground truth using controlled datasets. Our model is designed to either successfully classify file fragments that contain hidden patterns and high dimensional features, or to gracefully fail if there are no patterns to be recognized. Our experimental results of the model that we built show high accuracy of 99.82%, 99.73%, and 99.6%, when classifying BZ2, PNG, and GZ against JPEG file fragments, respectively.