Abstract

Sorting is a fundamental process in nature, industry and commerce, where it serves as a necessary step in making numerous activities efficient. This project focuses on the mathematical analysis of a specialized sorting strategy, context directed block swapping (CDS), active in the genome maintenance pro- gram of certain ciliate species. When successful, CDS is the most efficient sorting strategy among all block swapping strategies. The exact obstacles to successful sortability by CDS are well understood, but the dynamics of the CDS strategy in the presence of these obstacles are poorly understood. This project, drawing on several fields of math- ematics, exploits game theory to analyze the dynamics of CDS in the presence of obstacles to sortability.

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The Mathematical Dynamics of Ciliate Gene Sorting Algorithms

Sorting is a fundamental process in nature, industry and commerce, where it serves as a necessary step in making numerous activities efficient. This project focuses on the mathematical analysis of a specialized sorting strategy, context directed block swapping (CDS), active in the genome maintenance pro- gram of certain ciliate species. When successful, CDS is the most efficient sorting strategy among all block swapping strategies. The exact obstacles to successful sortability by CDS are well understood, but the dynamics of the CDS strategy in the presence of these obstacles are poorly understood. This project, drawing on several fields of math- ematics, exploits game theory to analyze the dynamics of CDS in the presence of obstacles to sortability.