In education, sample characteristics can be complex due to the nested structure of students, teachers, classrooms, schools, and districts. In the past, not many considerations were given to such complex sampling schemes in statistical power analysis. More recently in the past two decades, however, education scholars have developed tools to conduct…

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…