Collaborative Research: The Topology of Functional Data on Random Metric Spaces, Graphs and Graphons

协作研究：随机度量空间、图和图子上函数数据的拓扑

基本信息

批准号：
1722995
负责人：
Washington Mio
金额：
$ 35.49万
依托单位：
Florida State University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2017
资助国家：
美国
起止时间：
2017-08-15 至 2021-07-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1722995&HistoricalAwards=false
关键词：
Collaborative Research Topology Functional Data

项目摘要

Extracting, modeling, conceptualizing, and visualizing information residing in complex datasets in actionable form are core themes in modern data analysis. This project will take up these challenges in the broad realm of functional data, as they permeate the sciences and practical applications. The project will develop mathematical methods and computational tools that help us execute these tasks and establish a pipeline from functional data to actionable knowledge. There is a vast landscape of potential uses of these methods. Examples include analyses of dynamical social networks, understanding variation in the spatial profile of gene expression to enable studies of associations with health and developmental outcomes, and exploratory studies that interrogate microbiome and metabolomic networks. The project will leverage techniques from topological data analysis (TDA) to further develop and extend persistent homology and integrate TDA with probabilistic methods. This will enable development of methods and tools for probing structural variation in functions defined on random domains. The project will develop topological methods, computational tools, and their foundations to summarize, analyze, and visualize functional data on random compact metric spaces, networks and graphons, and establish a pipeline from such data to actionable knowledge. The advances resulting from the project will open many new perspectives in practical applications and research in such disciplines as developmental and evolutionary biology, medicine, social sciences, and engineering. Though powered by state-of-the-art methods, the resulting tools will be simple to use so as to attain broad utility. To enhance this important aspect of the project, by way of interdisciplinary collaboration with domain scientists, the methods will be tested on case studies that involve analyses of plant shape, rock micro-structure, and human microbiome data. The methods and software tools resulting from this project will be documented and distributed online for use by the research community further broadening the impact on other disciplines. The project also will generate resources to support several outreach activities.

以可行形式的复杂数据集中的提取，建模，概念化和可视化信息是现代数据分析中的核心主题。该项目将在功能数据的广泛领域中承担这些挑战，因为它们渗透到了科学和实际应用。该项目将开发数学方法和计算工具，以帮助我们执行这些任务，并建立从功能数据到可操作知识的管道。这些方法有广阔的景观。例子包括对动态社交网络的分析，了解基因表达的空间谱的变化，以使与健康和发展结果的关联进行研究，以及审查微生物组和代谢组网络的探索性研究。该项目将利用拓扑数据分析（TDA）的技术进一步发展和扩展持续的同源性，并将TDA与概率方法整合在一起。这将实现开发方法和工具，以探测随机域定义的功能的结构变化。该项目将开发拓扑方法，计算工具及其基础，以总结，分析和可视化随机紧凑的度量空间，网络和图形的功能数据，并建立从此类数据到可操作知识的管道。该项目所带来的进步将在开发和进化生物学，医学，社会科学和工程等学科的实际应用和研究中开放许多新的观点。尽管由最先进的方法提供动力，但最终的工具将易于使用，以实现广泛的实用程序。为了通过与领域科学家的跨学科合作来增强项目的这一重要方面，将在案例研究上测试这些方法，该案例研究涉及植物形状，岩石微观结构和人类微生物组数据的分析。该项目产生的方法和软件工具将在线记录和分发，以供研究社区使用，进一步扩大对其他学科的影响。该项目还将生成资源以支持几项外展活动。