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

算法是几乎所有计算技术的核心。应用范围从计算的基础设施到高度复杂的系统，如DNA测序。计算机算法的进步表现为(i)评估现有算法的性能，以提高我们对它们的理解，并更好地告知在各种竞争性算法中需要做出的选择，（ii）为新应用创建算法，以及（iii）扩展算法设计和分析的方法。计算机科学中的重要问题包括排序和搜索、有效的数据存储和数据压缩。要决定什么是在某些数据库中搜索给定项的好方法，或者用最少的内存存储音乐或视频的好方法，分析方法或算法是很重要的。涉及“算法分析”的问题通常可以简化为求解某类方程。研究者及其同事应开发数学工具来获得这些方程的解，无论是精确的解还是精确的近似值。相关的数学问题出现在其他重要领域，如分子生物学和通信，研究人员的方法和结果应该可以应用于广泛的问题。

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.