Computational learning theory studies the design and analysis of learning algorithms, and it is integral to the foundation of machine learning. In the modern era, classical computational learning theory is growingly unable to catch up with new practical demands. In particular, problems arise in the following aspects: i). "scalability":…

This dissertation explores bridge n-sections of knotted surfaces in 4-manifolds by defining invariants that measure the complexity of their topology and by giving geometric constructions that determine Lagrangian surfaces in 4-manifolds under certain conditions. First, we present an elegant geometric construction that generates all triple grid…

Graph neural networks (GNN) are vital for analyzing real-world problems (e.g., network analysis, drug interaction, electronic design automation, e-commerce) that use graph models. However, efficient GNN acceleration faces with multiple challenges related to high and variable sparsity of input feature vectors, power-law degree distribution in the…

This two-part dissertation centers on a re-examination of the role of book indexes in information retrieval research on full-text digital book collections in digital libraries. Early research focused on information retrieval and book indexes (in addition to other parts of books) in the 2000s when the Google Books corpus was first released to the…

The ideas of measurement and measurement comparisons (e.g., fractions, ratios, quotients) are introduced to students in elementary school. However, studies report that students of all ages have difficulty comparing two quantities in terms of their relative size. Students often understand fractions such as 3/7 as part-whole relationships or…

Authors of calculus texts often include graphs in the text with the intent that the graph depicts relationships described in theorems and formulas. Similarly, graphs are often utilized in classroom lectures and discussions for the same purpose. The author or instructor includes function graphs to represent quantitative relationships and how a pair…

Graph data, especially large graph data, come up in many domains, such as social networks, the map of science, biological data, and even knitting! This presents a problem when we consider visualizing these structures. Layouts must be chosen carefully so that the structure of the graph is visible. Some graphs are large enough and connected enough…

Graph Signal Processing (GSP) plays a crucial role in addressing the growing need for information processing across networks, especially in tasks like supervised classification. However, the success of GSP in such tasks hinges on accurately identifying the underlying relational structures, which are often not readily available and must be inferred…

All chemistry students must develop competency in analyzing and making sense of data. However, there are many difficulties that chemistry students may experience while analyzing data. Many students may not use relevant prior knowledge to aid in making sense of data, or they may not form conclusions using all the data provided. Additionally, prior…

Laboratory activities are a prevalent and essential part of chemistry learning because of their potential to help students develop problem solving abilities, visualize chemistry concepts learned in lecture, and gain practical skills. However, learning in the laboratory environment is not without its challenges. For example, cookbook-style…

Several daily phenomena around us can be modeled as time-evolving networks. Working with expressive and tractable models for the evolution of such networks can improve different prediction and decision-making tasks. While the literature has studied many approaches to model such networked phenomena partially, multiple gaps remain. This thesis is an…

This qualitative case study pursued to describe the different strategies Mexican American adult students in a local community college used to graph function transformations. Participants in the study were purposefully selected using a criterion sampling to ensure participants were atypical, above average students between the ages 18-22, and had a…

This study applies human-centered design principles and involves end users in creating a usable knowledge graph. The aim was to explore the potential advantages of capturing and presenting networked knowledge in a domain for information discovery and decision-making purposes. The case taken for the research is the interdisciplinary Ph.D. program…

Current network design problems can be solved by offline or online methods. Offline methods are criticized for their complexity and in flexibility, whereas online methods lack guaranteed optimality. Non-blocking properties, which are typically studied in switching structures, could be used to evaluate the capability of a switching structure to…

Online networks, as digital images reflecting every aspects of real world especially under the current context of information technology, have become the most massive and opulent data source these days, where vast amount of information keeps being produced and transmitted. Their rapid expansion in scale and data volume draws wide attention and…