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Textures are used widely in computer graphics to represent fine visual details and produce realistic looking images. Often it is necessary to remove some foreground object from the scene. Removal of the portion creates one or more holes in the texture image. These holes need to be filled to complete the image. Various methods like clone brush strokes and compositing processes are used to carry out this completion. User skill is required in such methods. Texture synthesis can also be used to complete regions where the texture is stationary or structured. Reconstructing methods can be used to fill in large-scale missing regions by interpolation. Inpainting is suitable for relatively small, smooth and non-textured regions. A number of other approaches focus on the edge and contour completion aspect of the problem. In this thesis we present a novel approach for addressing this image completion problem. Our approach focuses on image based completion, with no knowledge of the underlying scene. In natural images there is a strong horizontal orientation of texture/color distribution. We exploit this fact in our proposed algorithm to fill in missing regions from natural images. We follow the principle of figural familiarity and use the image as our training set to complete the image.

The focus of this research study was to determine how elementary students enrolled in virtual education classes performed on state assessments and final report card grades in Reading and Mathematics as compared with students enrolled in traditional classes, and to examine whether there was a difference in the successful course completion rates between the two groups. Five research questions guided this study concerning the relationship of successful course completion, final grades, and FCAT 2.0 achievement level scores and the variables of virtual and traditional education in the School District of Volusia County. This study is significant, as the movement of virtual learning is driven by economic factors and learning outcomes need to be considered in making instructional delivery decisions. Chi-square analysis suggested no statistical significant difference existed in either Reading or Mathematics successful course completion of students in virtual and traditional settings. Chi-square analyses and a one-sample t-test suggested there was no statistical significant difference in performance of virtual and traditional students on FCAT 2.0 Reading and Mathematics achievement levels. Although the Chi-square analyses showed no statistical significance in performance of virtual and traditional students on final report card grades in Reading and Mathematics, the one-sample t-tests suggested there was a statistically significant difference. When interpreting these results, caution should be taken as the virtual student population was extremely disproportionate to the traditional student population. Implications for practice and recommendations for future study are suggested in this study

Baccalaureate degree completion statistics are surprisingly low. National four-year graduation rates hover around 38%, and six-year graduation rates have remained steady at approximately 63% (Berkner, He, & Cataldi, 2002). At the University of Central Florida, as at many public research institutions, the numbers are even lower. Literature has emerged, however, which suggests that students who participate in cooperative education programs may experience increased motivation to continue the formal education process (Avenoso & Totoro, 1994; Schambach & Dirks, 2002; Somers, 1986). This study investigated the effect of co-op participation on undergraduate degree completion in the context of several risk factors for attrition. The population for this study was the cohort of full-time, bachelor's degree-seeking undergraduate students who entered the University of Central Florida as first-time-in-college (FTIC) students in the fall semester of 1999. Group One (Co-op Students) consisted of full-time FTIC students who successfully participated in the University of Central Florida Cooperative Education program and Group Two (Non-Participants) included full-time FTIC students with at least 20 credit hours completed and consistent grade point averages of at least 2.5 who did not participate in the University of Central Florida Cooperative Education program. The additional parameters on the Non-Participant group were included to control for any potential differences between the two groups due to increased requirements for participation in the co-op program. The two groups arrived at the University of Central Florida with nearly identical high school grade point averages and standardized test scores, and also were remarkably similar in age, ethnic composition, and college at entry. Results indicated that students who graduated within four years seemed to do so regardless of co-op participation, but for those who took longer, there was a correlation between co-op and degree completion. There was also some evidence to suggest that internships are associated with degree completion as well. Further, some of the known risk factors for attrition (lower high school grade point average, male gender, and non-White/non-Asian ethnicity) may be mitigated by the student's participation in their institution's co-op program, though additional research in this area is suggested.

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Felix Mendelssohn-Bartholdy hat neben fünf vollständigen Symphonien das Fragment des ersten Satzes einer letzten Symphonie in C-Dur hinterlassen, an dem er zwei Jahre vor seinem Tod letztmalig arbeitete. Führt man sich Mendelssohns Arbeitsweise vor Augen, die lange Unterbrechungen des Kompositionsprozesses eines Werkes miteinschloss, erscheint es gut möglich, dass der Komponist die Arbeit an diesem Sinfoniesatz noch einmal wieder aufgenommen hätte. 2002, im letzten Jahr meines Studiums an der Hochschule für Musik und Theater Felix Mendelssohn-Bartholdy Leipzig habe ich dieses Fragment im Stil Mendelssohns vervollständigt und aufführbar macht. Im folgenden Text erörtere ich meinen Umgang mit dem Fragment, begründe wichtige formale Entscheidungen und stelle Ausschnitte aus der Partitur vor. Eine Präsentation meiner Arbeit im Rahmen eines Werkstattkonzerts – im Fall einer solchen, stilistisch einheitlichen Vervollständigung wünschenswert, um den Anteil authentischer und ergänzter Passagen genau offenzulegen – wäre von diesen und weiteren Ausführungen begleitet, und böte so Gelegenheit, einem Konzertpublikum auf anschauliche Weise Aspekte musiktheoretischen Denkens zu vermitteln. / Besides five complete symphonies, Felix Mendelssohn-Bartholdy left behind a fragment of the first movement of a last symphony in C major on which he last worked two years before his death. Following examination of Mendelssohn’s modus operandi, which included long interruptions in the compositional process, it seems entirely possible that he in fact returned to work on this movement. In the final year of my study at the Hochschule für Musik und Theater Felix Mendelssohn-Bartholdy in Leipzig I completed this fragment in Mendlessohn’s style and made it available for performance. In the following article I defend my approach to the fragment, justify important formal decisions, and present excepts from the score. A presentation of my work in the context of a workshop-concert – ideally a stylistically consistent completion in order to clearly differentiate between authentic and added passages – would be accompanied by these and other considerations, and would offer an opportunity to communicate music-theoretical concepts to a general public in an approachable manner.

This qualitative case study was completed at a rural medium-sized Texas community college and sought to understand how advisors and program coordinators made sense of the 60X30TX policy as it was implemented at their institution. The theoretical framework included community college, the Completion Agenda, structure-agency, and sensemaking. Each community college has its own culture shaped from its history, open access, policies, employees, and students. But the community college is influenced by the state with its mandates and policies, which results in a structure-agency relationship in which the state defines and sets higher education goals, while the community college strives to meet those goals in the way it determines best. The Completion Agenda has influenced state policies shifting the focus of higher education from access to access and completion. The state policy is a catalyst for change at the institution, but change cannot exist without sensemaking. As change occurs, people begin to interpret it based on the environment and their individual and group experiences. Sensemaking becomes central to the theoretical framework with the community college, the structure-agency relationship, and the Completion Agenda. Interviews with 12 people identified four themes: culture of completion, rebuilding advising, dual credit, and Pathways program impact. Participants embraced the completion goal of 60X30TX since it mapped to the college's mission and goals. Advising was reinvented to focus on the student holistically. Dual credit and the Pathways program were strategies of 60X30TX and were reflected at ACC. Both had benefits to the students, but also had consequences.

<p dir="ltr">In most theoretical studies on missing data analysis, data is typically assumed to be missing according to a specific probabilistic model. However, such assumption may not accurately reflect real-world situations, and sometimes missing is not purely random. In this thesis, our focus is on analyzing incomplete data matrices without relying on any probabilistic model assumptions for the missing schemes. To characterize a missing scheme deterministically, we employ a graph whose adjacency matrix is a binary matrix that indicates whether each matrix entry is observed or not. Leveraging its graph properties, we mathematically represent the missing pattern of an incomplete data matrix and conduct a theoretical analysis of how this non-random missing pattern affects the solvability of specific problems related to incomplete data. This dissertation primarily focuses on three types of incomplete data problems characterized by their low-rank nature: structured prediction, matrix completion, and sparse PCA.</p><p dir="ltr">First, we investigate a basic structured prediction problem, which involves recovering binary node labels on a fixed undirected graph, where noisy binary observations corresponding to edges are given. Essentially, this setting parallels a simple binary rank-1 symmetric matrix completion problem, where missing entries are determined by a fixed undirected graph. Our aim is to establish the fundamental limit bounds of this problem, revealing a close association between the limits and graph properties, such as connectivity.</p><p dir="ltr">Second, we move on to the general low-rank matrix completion problem. In this study, we establish provable guarantees for exact and approximate low-rank matrix completion problems that can be applied to any non-random missing pattern, by utilizing the observation graph corresponding to the missing scheme. We theoretically and experimentally show that the standard constrained nuclear norm minimization algorithm can successfully recover the true matrix when the observation graph is well-connected and has similar node degrees. We also verify that matrix completion is achievable with a near-optimal sample complexity rate when the observation graph has uniform node degrees and its adjacency matrix has a large spectral gap.</p><p dir="ltr">Finally, we address the sparse PCA problem, featuring an approximate low-rank attribute. Missing data is common in situations where sparse PCA is useful, such as single-cell RNA sequence data analysis. We propose a semidefinite relaxation of the non-convex $\ell_1$-regularized PCA problem to solve sparse PCA on incomplete data. We demonstrate that the method is particularly effective when the observation pattern has favorable properties. Our theory is substantiated through synthetic and real data analysis, showcasing the superior performance of our algorithm compared to other sparse PCA approaches, especially when the observed data pattern has specific characteristics.</p>

Machine learning (ML) has enjoyed great success in chemistry and drug design, from designing synthetic pathways to drug screening, to biomolecular property predictions, etc.. However, ML model's generalizability and robustness require high-quality training data, which is often difficult to obtain, especially when the training data is acquired from experimental measurements. While one can always discard all data associated with noisy and/or missing values, this often results in discarding invaluable data. This thesis presents and applies mathematical techniques to solve this problem, and applies them to problems in molecular medicinal chemistry. In chapter 1, we indicate that the missing-data problem can be expressed as a matrix completion problem, and we point out how frequently matrix completion problems arise in (bio)chemical problems. Next, we use matrix completion to impute the missing values in protein-NMR data, and use this as a stepping-stone for understanding protein allostery in Chapter 2. This chapter also used several other techniques from statistical data analysis and machine learning, including denoising (from robust principal component analysis), latent feature identification from singular-value decomposition, and residue clustering by a Gaussian mixture model. In chapter 3, Δ-learning was used to predict the free energies of hydration (Δ𝐺). The aim of this study is to correct estimated hydration energies from low-level quantum chemistry calculations using continuum solvation models without significant additional computation. Extensive feature engineering, with 8 different regression algorithms and with Gaussian process regression (38 different kernels) were used to construct the predictive models. The optimal model gives us MAE of 0.6249 kcal/mol and RMSE of 1.0164 kcal/mol. Chapter 4 provides an open-source computational tool Procrustes to find the maximum similarities between metrics. Some examples are also given to show how to use Procrustes for chemical and biological problems. Finally, in Chapters 5 and 6, a database for permeability of the blood-brain barrier (BBB) was curated, and combined with resampling strategies to form predictive models. The resulting models have promising performance and are released along with a computational tool B3clf for its evaluation. / Thesis / Doctor of Science (PhD)

Troup County, Georgia has been afflicted with elevated teen pregnancy and subsequent teen pregnancy rates. As a result, Circle of Care was developed to reduce the subsequent teen pregnancy rate within Troup County. Circle of Care works with pregnant and parenting teens and their families to enhance their quality of life. A case manager provides information, education and support to enable the teens to stay in school, prevent subsequent teen pregnancies, and prevent child abuse and neglect. This study evaluates the effectiveness of Circle of Care by determining if intensity and duration of program participation have an impact on achieving the desired outcomes for program participants. The results of this research suggest that Circle of Care is reducing subsequent teen pregnancies, increasing educational attainment and decreasing child abuse and neglect among program participants.