Collaborative Research: Nonlinear Equations Arising in Information Theory and Computer Sciences

点击翻译按钮获取中文摘要

Algorithms are at the heart of virtually all computing technologies. Applications range from the infrastructure of computing to highly complex systems such as DNA sequencing. Advances in computer algorithms take the form of (i) evaluating the performance of existing algorithms so as to improve our understanding of them, and to better inform the choices that need to be made among various competitive algorithms, (ii) creating algorithms for new applications, and (iii) expanding the methodology of algorithm design and analysis. Important problems in computer science include sorting and searching, efficient data storage, and data compression. To decide on what is a good method to search out a given item in some database, or a good method for storing music or video with minimal use of memory, it is important to analyze the method or algorithm. Questions involving the "analysis of algorithms" can frequently be reduced to solving certain classes of equations. The investigator and colleagues shall develop mathematical tools for obtaining solutions of these equations, either exact ones or accurate approximations. Related mathematical problems arise in other important areas such as molecular biology and communications, and the investigators' methods and results should find applications to a wide range of problems.