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- ItemThe Effect of Behavioral Objectives on Measures of Learning and Forgetting on High School Algebra(1972) Loh, Elwood Lockert; Walbesser, Henry H.; Mathematics and Education; Digital Repository at the University of Maryland; University of Maryland (College Park, MD)During the past decade, the number of educators who advocate the use of behavioral objectives in education has increased. The increase in the number of advocates of behavioral objectives has been followed by an increasing awareness of the need for empirical research to give credence to such a viewpoint. At present, there is not a substantial number of research studies in which behavioral objectives have been used as a manipulated variable. In previously reported learning studies in which behavioral objectives have been used as an experimental variable, measures of learning and measures of forgetting have been derived from achievement scores. The results obtained in the learning studies have not been singular in support of the use of behavioral objectives, however, the results obtained in forgetting studies have consistently supported their use. This two part study investigated the effect of presenting behavioral objectives to students during the initial phase of a learning program. There were six criterion variables observed: index of learning, rate of learning, index of forgetting, rate of forgetting, index of retention, and index of efficiency. Two 2-year algebra one classes with a total of 52 students were randomly partitioned into two treatment groups for the learning phase of the study. The classes were further randomly partitioned into three retention groups for the forgetting phase of the study. The instructional materials were programmed within the framework of a learning hierarchy. The use of the learning hierarchy facilitated the use of a procedure for separating behaviors not yet possessed by a student from behaviors previously acquired. This was accomplished by presenting students with preassessment tasks prior to instruction for a behavior in the learning hierarchy. If the subject's response to the preassessment task indicated that he possessed the behavior, instruction was not given for that behavior. If the response indicated that the subject had not previously acquired the behavior, instruction was presented. The measures of the time needed to acquire the behavior were subsequently used to compute the six experimental measures. Three retention periods of 7 calendar days, 14 calendar days, and 15 to 21 calendar days were used for the forgetting phase of the study. The results of the three retention periods were pooled for the two forgetting measures, the index of retention, and the index of efficiency. The data collected in the study were analyzed by six separate tests using a one-way analysis of variance. A 0.05 level of significance was used for each of the six tests. The following results were obtained: 1. The index of learning for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of learning for students who were not so informed. 2. The rate of learning for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the rate of learning for students who were not so informed. 3. The index of forgetting for students who were informed of behavioral objectives during the initial phases of the learning program was not less than the index of forgetting for students who were not so informed. 4. The rate of forgetting for students who were informed of behavioral objectives during the initial phases of the learning program was not less than the rate of forgetting for students who were not so informed. 5. The index of retention for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of retention for students who were not so informed. 6. The index of efficiency for students who were informed of behavioral objectives during the initial phases of the learning program was not greater than the index of efficiency for students who were not so informed. It was concluded that the results of the study do not support the use of behavioral objectives as a procedure for improving either measures of learning or measures of forgetting which are functions of the time needed to reach criterion in a learning program using programmed instruction for teaching an algebraic topic to below average mathematics students in senior high school. It was recommended that further research is needed to determine a reliable and valid procedure for measuring learning and forgetting. It was also recommended that alternatives to programmed instruction be considered for learning and forgetting studies.
- ItemDISSECTING TUMOR CLONALITY IN LIVER CANCER: A PHYLOGENY ANALYSIS USING COMPUTATIONAL AND STATISTICAL TOOLS(2023) Kacar, Zeynep; Slud, Eric ES; Levy, Doron DL; Mathematical Statistics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Liver cancer is a heterogeneous disease characterized by extensive genetic and clonaldiversity. Understanding the clonal evolution of liver tumors is crucial for developing effective treatment strategies. This dissertation aims to dissect the tumor clonality in liver cancer using computational and statistical tools, with a focus on phylogenetic analysis. Through advancements in defining and assessing phylogenetic clusters, we gain a deeper understanding of the survival disparities and clonal evolution within liver tumors, which can inform the development of tailored treatment strategies and improve patient outcomes. The thesis begins by providing an overview of sources of heterogeneity in liver cancer and data types, from Whole-Exome (WEX) and RNA sequencing (RNA-seq) read-counts by gene to derived quantities such as Copy Number Alterations (CNAs) and Single Nucleotide Variants (SNVs). Various tools for deriving copy-numbers are discussed and compared. Additionally, comparison of survival distributions is discussed. The central data analyses of the thesis concern the derivation of distinct clones and clustered phylogeny types from the basic genomic data in three independent cancer cohorts, TCGA-LIHC, TIGER-LC and NCI-MONGOLIA. The SMASH (Subclone multiplicity allocation and somatic heterogeneity) algorithm is introduced for clonality analysis, followed by a discussion on clustering analysis of nonlinear tumor evolution trees and the construction of phylogenetic trees for liver cancer cohorts. Identification of drivers of tumor evolution, and the immune cell micro-environment of tumors are also explored. In this research, we employ survival analysis tools to investigate and document survival differences between groups of subjects defined from phylogenetic clusters. Specifically, we introduce the log-rank test and its modifications for generic right-censored survival data, which we then apply to survival follow-up data for the subjects in the studied cohorts, clustered based on their genomic data. The final chapter of this thesis takes a significant step forward by extending an existing methodology for covariate-adjustment in the two-sample log-rank test to a K-sample scenario, with a specific focus on the already defined phylogeny cluster groups. This extension is not straightforward because the computation of the test statistic for K-sample and its asymptotic null distribution do not follow directly from the two-sample case. Using these extended tools, we conduct an illustrative data analysis with real data from the TIGER-LC cohort, which comprises subjects with analyzed and clustered genomic data, leading to defined phylogenetic clusters associated with two different types of liver cancer. By applying the extended methodology to this dataset, we aim to effectively assess and validate the survival curves of the defined clusters.
- ItemNEW STATISTICAL METHODS FOR HIGH-DIMENSIONAL INTERCONNECTED DATA WITH UNIFORM BLOCKS(2023) Yang, Yifan; Chen, Shuo; Mathematics; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)Empirical analyses of high-dimensional biomedical data, including genomics, proteomics, microbiome, and neuroimaging data, consistently reveal the presence of strong modularity in the dependence patterns. In these analyses, highly correlated features often form a few distinct communities or modules, which can be interconnected with each other. While the interconnected community structure has been extensively studied in biomedical research (e.g., gene co-expression networks), its potential to assist in statistical modeling and inference remains largely unexplored. To address this research gap, we propose novel statistical models and methods that capitalize on the prevalent community structures observed in large covariance and precision matrices derived from high-dimensional biomedical interconnected data. The first objective of this dissertation is to delve into the algebraic properties of the proposed interconnected community structures at the population level. Specifically, this pattern partitions the population covariance matrix into uniform (i.e., equal variances and covariances) blocks. To accomplish this objective, we introduce a block Hadamard product representation in Chapter 2, which relies on two lower-dimensional "coordinate" matrices and a pre-specific vector.This representation enables the explicit expressions of the square or power, determinant, inverse, eigendecomposition, canonical form, and the other matrix functions of the original larger-dimensional matrix on the basis of these lower-dimensional "coordinate" matrices. Estimating a covariance matrix is central to high-dimensional data analysis. Our second objective is to consistently estimate a large covariance or precision matrix having an interconnected community structure with uniform blocks. In Chapter 3, we derive the best-unbiased estimators for covariance and precision matrices in closed forms and provide theoretical results on their asymptotic properties. Our proposed method improves the accuracy of covariance and precision matrix estimation and demonstrates superior performance compared to the competing methods in both simulations and real data analyses. In Chapter 4, our goal is to investigate the effects of alcohol intake (as an exposure) on metabolomics outcome features. However, similar to other omics data, metabolomic outcomes often consist of numerous features that exhibit a structured dependence pattern, such as a co-expression network with interconnected modules. Effectively addressing this dependence structure is crucial for accurate statistical inferences and the identification of alcohol intake-related metabolomic outcomes. Nevertheless, incorporating the structured dependence patterns into multivariate outcome regression models remains difficulties in accurate estimation and inference. To bridge this gap, we propose a novel multivariate regression model that accounts for the correlations among outcome features using a network structure composed of interconnected modules. Additionally, we derive closed-form estimators of regression parameters and provide inference tools. Extensive simulation analysis demonstrates that our approach yields much-improved sensitivity with a well-controlled discovery rate when benchmarking against existing multivariate regression models. Confirmatory factor analysis (CFA) models play a crucial role in revealing underlying latent common factors within sets of correlated variables. However, their implementation often relies on a strong prior theory to categorize variables into distinct classes, which is frequently unavailable (e.g., in omics data analysis scenarios). To address this limitation, in Chapter 5, we propose a novel strategy based on network analysis that allows data-driven discovery to substitute for the lacking prior theory. By leveraging the detected interconnected community structure, our approach offers an elegant statistical interpretation and yields closed-form uniformly minimum variance unbiased estimators for all unknown matrices. To evaluate the effectiveness of our proposed estimation procedure, we compare it to conventional numerical methods and thoroughly validate it through extensive Monte Carlo simulations and real-world applications.
- ItemAdversarial Robustness and Fairness in Deep Learning(2023) Cherepanova, Valeriia; Goldstein, Tom; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)While deep learning has led to remarkable advancements across various domains, the widespread adoption of neural network models has brought forth significant challenges such as vulnerability to adversarial attacks and model unfairness. These challenges have profound implications for privacy, security, and societal impact, requiring thorough investigation and development of effective mitigation strategies. In this work we address both these challenges. We study adversarial robustness of deep learning models and explore defense mechanisms against poisoning attacks. We also explore the sources of algorithmic bias and evaluate existing bias mitigation strategies in neural networks. Through this work, we aim to contribute to the understanding and enhancement of both adversarial robustness and fairness of deep learning systems.
- ItemDecentralized Transportation Model In Vehicle Sharing(2023) Li, Ying; Ryzhov, Ilya; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)This dissertation introduces the concept of decentralization to address the rebalancing challenges in bike-sharing systems and proposes a model known as the Decentralized Route Assignment Problem (DRAP) under specific assumptions. The primary contributions of this research include the formulation of the DRAP and the derivation of theoretical results that facilitate its transformation into a lower-dimensional global optimization problem. This transformation enables efficient exploration using modern search methods. An extended version of DRAP, called DRAP-EA, is also proposed for further analysis by introducing more agents into the system. Various solution approaches, such as branch-and-cut, hill-climbing, and simulated annealing, are explored and customized to enhance their performance in the context of rebalancing. Two simulated annealing methods, Gurobi with warm-start, and an extension of the local search algorithm are implemented on 24 instances derived from a comprehensive case study for experimental evaluation. The experimental results consistently demonstrate the superior performance of the simulated annealing methods. Furthermore, a comparison between SA and SA-PS is conducted, and the obtained solutions are visualized to help further explore the spatial patterns and traffic flows within the bike-sharing system.