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Partitions Of Finite Frames, James Michael Rosado
Partitions Of Finite Frames, James Michael Rosado
Theses and Dissertations
An open question stated by Marcus, Spielman, and Srivastava [10] asks "whether one can design an efficient algorithm to find the partitions guaranteed by Corollary 1.5." This corollary states that given a set of vectors in C whose outer products sum to the identity there exists a partition of these vectors such that norms of the outer-product sums of each subset satisfy an inequality bound. Here particular types of vector sets called finite frames are analyzed and constructed to satisfy the inequality described in Corollary 1.5. In this thesis, rigorous proofs and formulations of outer-product norms are utilized to find …
Evaluating And Improving The Efficiency Of Software And Algorithms For Sequence Data Analysis, Hugh L. Eaves
Evaluating And Improving The Efficiency Of Software And Algorithms For Sequence Data Analysis, Hugh L. Eaves
Theses and Dissertations
With the ever-growing size of sequence data sets, data processing and analysis are an increasingly large portion of the time and money spent on nucleic acid sequencing projects. Correspondingly, the performance of the software and algorithms used to perform that analysis has a direct effect on the time and expense involved. Although the analytical methods are widely varied, certain types of software and algorithms are applicable to a number of areas. Targeting improvements to these common elements has the potential for wide reaching rewards. This dissertation research consisted of several projects to characterize and improve upon the efficiency of several …