Persistent Homology, Metrics, and Applications on the Collection of Enriched Metric Measure Spaces

丰富度量测度空间集合上的持久同源性、度量和应用

• 批准号: 2138110
• 负责人: Ranthony Edmonds
• 金额: $ 30万
• 依托单位: Edmonds, Ranthony A C
• 依托单位国家: 美国
• 项目类别: Fellowship Award
• 财政年份: 2022
• 资助国家: 美国
• 起止时间: 2022-01-01 至 2025-05-31
• 项目状态: 未结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=2138110&HistoricalAwards=false
• 关键词: Persistent; Homology; Metrics; Applications; Collection

This award is made as part of the FY 2021 Mathematical and Physical Sciences Ascending Postdoctoral Research Fellowships, MPS-Ascend Program. Ranthony Edmonds is awarded this fellowship to conduct a program of research and education at the Ohio State University in the mathematical sciences, including applications to other disciplines, under the mentorship of the sponsoring scientist Facundo Memoli. This project is devoted to some challenging issues of topological data analysis (TDA), a new and rapidly growing field that leverages tools from algebraic topology and many other areas to study the shape of big data. Along with this research, Edmonds will develop educational activities related to data science in collaboration with existing partnerships with local and national networks focused on increasing representation of underrepresented minorities in the mathematical sciences.The project has several objectives. The first is the study of metric measure spaces, and finding an appropriate notion for the Gromov-Wasserstein (GW) distance. The second goal is to explore stability of data under small perturbations in the GW distance. The third goal is applied and concerns electoral redistricting where the basic idea is to use the GW metric to compare redistricting plans.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.

该奖项是作为2021财年数学和物理科学上升博士后研究奖学金，MPS-Ascend计划的一部分。兰尼埃德蒙兹被授予这项奖学金进行研究和教育计划在俄亥俄州州立大学的数学科学，包括应用到其他学科，指导下的赞助科学家法昆多梅莫利。该项目致力于拓扑数据分析（TDA）的一些具有挑战性的问题，这是一个新的快速发展的领域，利用代数拓扑和许多其他领域的工具来研究大数据的形状。沿着这项研究，埃德蒙兹将与当地和国家网络的现有合作伙伴合作，开发与数据科学相关的教育活动，重点是增加数学科学中代表性不足的少数民族的代表性。该项目有几个目标。第一个是研究度量测度空间，并为Gromov-Wasserstein（GW）距离找到一个合适的概念。 第二个目标是探索在GW距离的小扰动下数据的稳定性。第三个目标是应用和涉及选举选区重划的基本思想是使用GW指标比较重划计划。这个奖项反映了NSF的法定使命，并已被认为是值得通过使用基金会的智力价值和更广泛的影响审查标准进行评估的支持。

项目成果

Aggregating community maps

• DOI: 10.1145/3557915.3560961
• 发表时间: 2022-11
• 期刊: Proceedings of the 30th International Conference on Advances in Geographic Information Systems
• 作者: E. Chambers;M. Duchin;Ranthony A. C. Edmonds;Parker B. Edwards;JN Matthews;Anthony E. Pizzimenti;Chanel Richardson;Parker Rule;Ari Stern