Algebraic algorithms for Cell Complexes: Incubation Activity

细胞复合体的代数算法：孵化活动

• 批准号: 0138323
• 负责人: Reinhard Laubenbacher
• 金额: $ 10万
• 依托单位: Virginia Polytechnic Institute and State University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-05-01 至 2004-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0138323&HistoricalAwards=false
• 关键词: Algebraic; algorithms; Cell; Complexes; Incubation

DMS-0138323Reinhard C. LaubenbacherThis award supports research concerned with the algorithmicrepresentation of cell complexes, a special type of topological space. These complexes arise as topological models of data and processes in science and engineering. Specific applications of interest are to biological, social, and communications networks, as well as to problems in statistics. Topological invariants of the complexes provide measures of certain characteristics of the processes producing the data. The use of cell complexes as data models represents a new application of these structures to science and engineering network problems. The methods employed include tools from computational algebra, combinatorics, and combinatorial topology, thereby making a contribution to the applicability of new mathematical areas to some pressing and challenging applied problems. Research results will be disseminated directly to the end user outside the mathematical community. The project impacts a number of graduate students, including students from underrepresented groups.

DMS-0138323Reinhard C. Laubenbacher 该奖项支持与细胞复合体（一种特殊类型的拓扑空间）的算法表示有关的研究。 这些复合体作为科学和工程中数据和过程的拓扑模型而出现。 感兴趣的具体应用是生物、社会和通信网络，以及统计问题。 复合体的拓扑不变量提供了对产生数据的过程的某些特征的测量。 使用细胞复合体作为数据模型代表了这些结构在科学和工程网络问题中的新应用。 所采用的方法包括计算代数、组合数学和组合拓扑的工具，从而为新的数学领域对一些紧迫和具有挑战性的应用问题的适用性做出了贡献。 研究结果将直接传播给数学界之外的最终用户。 该项目影响了许多研究生，包括来自代表性不足群体的学生。