Algebraic algorithms for Cell Complexes: Incubation Activity

DMS-0138323莱因哈德·C·劳本巴赫该奖项支持与细胞复合体的算法表示有关的研究，细胞复合体是一种特殊类型的拓扑空间。这些复合体作为科学和工程中的数据和过程的拓扑模型而出现。令人感兴趣的具体应用是生物、社会和通信网络，以及统计学中的问题。复合体的拓扑不变量提供了产生数据的过程的某些特征的度量。细胞复合体作为数据模型的使用代表了这些结构在科学和工程网络问题上的新应用。所采用的方法包括计算代数、组合数学和组合拓扑学的工具，从而有助于将新的数学领域应用于一些紧迫和具有挑战性的应用问题。研究成果将直接传播给数学界以外的最终用户。该项目影响了一些研究生，包括来自代表性不足群体的学生。

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.