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…

Misinformation and rumors have become rampant on online social platforms with adverse consequences for the real world. Fact-checking efforts are needed to mitigate the risks associated with the spread of digital misinformation. However, the pace at which information is generated online limits the capacity to fact-check claims at the same rate…

Two problems at two different abstraction levels of computational biology are studied. At the molecular level, efficient pattern matching algorithms in DNA sequences are presented. For gene order data, an efficient data structure is presented capable of storing all gene re-orderings in a systematic manner. A common characteristic of presented…

With the rise of the internet, mobile communications, electronic transactions, and personal broadcasting, the scale of connectedness has grown immensely. Not only can an individual interact with thousands and millions of others, but details about those interactions are being stored in databases, for later retrieval and analysis. Two key concepts…

Graphs are widely used to model structures and relationships of objects in various scientific and commercial fields. Chemical molecules, proteins, malware system-call dependencies and three-dimensional mechanical parts are all modeled as graphs. In this dissertation, we propose to mine and index those graph data to enable fast and scalable search.…

Improving foundational academic skills for elementary level students continues to be a challenge for classroom teachers. This study implemented weekly progress monitoring procedures using curriculum-based measurement assessments in conjunction with weekly individual student-teacher graphing and goal-setting conferences to determine the effect the…

This thesis investigates and develops a few acceleration techniques for the search engine algorithms used in PageRank and HITS computations. PageRank and HITS methods are two highly successful applications of modern Linear Algebra in computer science and engineering. They constitute the essential technologies accounted for the immense growth and…