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CIF: Small: Bridging the Inequality Gap

CIF：小：缩小不平等差距

基本信息

批准号：
1907786
负责人：
Robert Nowak
金额：
$ 15万
依托单位：
University of Wisconsin-Madison
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2019
资助国家：
美国
起止时间：
2019-08-01 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1907786&HistoricalAwards=false
关键词：
CIF Small Bridging Inequality Gap

项目摘要

Inequalities are a vital component of information theory and comprise one of the most versatile mathematical tools in an information theorist's toolbox. Breakthroughs in obtaining strong information inequalities have invariably led to significant progress on longstanding open problems in information theory, and in turn contribute to the advancement of computer science, probability theory, and combinatorics. This project aims to advance the state-of-the-art knowledge of information inequalities by identifying and addressing key gaps in the existing literature. Being able to provide a better characterization of information inequalities and narrowing existing gaps can greatly increase our understanding of what is feasible in many computationally intractable problems in computer science and mathematics. The project will also support the educational goals of the investigator by training multiple graduate students working at the interface of engineering and mathematics.The project consists of a specific set of research questions that will uncover novel theoretical aspects of information inequalities and will lead to new mathematical strategies to establish novel inequalities. The work will be divided into the following sub-projects, each with a distinct set of research objectives: (1) Perform stability analyses of fundamental information inequalities; (2) Develop a principled approach for establishing new information inequalities by leveraging sub-additivity properties in information theory; and (3) Explore applications of stability results and proof strategies to areas beyond information theory, such as probability, queuing theory, and combinatorics.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

不等式是信息论的重要组成部分，也是信息论工具箱中最通用的数学工具之一。在获得强信息不平等的突破，总是导致重大进展的长期开放的问题，在信息理论，反过来又有助于计算机科学，概率论和组合学的进步。该项目旨在通过确定和解决现有文献中的关键差距，促进对信息不平等的最新了解。能够更好地描述信息不平等并缩小现有差距，可以大大提高我们对计算机科学和数学中许多计算棘手问题的可行性的理解。该项目还将通过培训多名工程和数学接口的研究生来支持研究人员的教育目标。该项目包括一组特定的研究问题，这些问题将揭示信息不平等的新理论方面，并将导致新的数学策略来建立新的不平等。这项工作将分为以下子项目，每个子项目都有一套独特的研究目标：（1）对基本信息不平等进行稳定性分析;（2）通过利用信息理论中的次可加性特性，制定建立新的信息不平等的原则性方法;以及（3）探索稳定性结果和证明策略在信息论以外的领域的应用，如概率论，排队论，该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。