| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | August 22, 2017 |
| Latest Amendment Date: | August 12, 2019 |
| Award Number: | 1722995 |
| Award Instrument: | Continuing Grant |
| Program Manager: |
Christopher Stark
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 15, 2017 |
| End Date: | July 31, 2021 (Estimated) |
| Total Intended Award Amount: | $354,912.00 |
| Total Awarded Amount to Date: | $354,912.00 |
| Funds Obligated to Date: |
FY 2018 = $117,518.00 FY 2019 = $122,547.00 |
| History of Investigator: |
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| Recipient Sponsored Research Office: |
874 TRADITIONS WAY TALLAHASSEE FL US 32306-0001 (850)644-5260 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
1017 Academic Way Tallahassee FL US 32306-4510 |
| Primary Place of
Performance Congressional District: |
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| Unique Entity Identifier (UEI): |
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| Parent UEI: |
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| NSF Program(s): | CDS&E-MSS |
| Primary Program Source: |
01001819DB NSF RESEARCH & RELATED ACTIVIT 01001920DB NSF RESEARCH & RELATED ACTIVIT |
| Program Reference Code(s): |
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| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
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.
PUBLICATIONS PRODUCED AS A RESULT OF THIS RESEARCH
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PROJECT OUTCOMES REPORT
Disclaimer
This Project Outcomes Report for the General Public is displayed verbatim as submitted by the Principal Investigator (PI) for this award. Any opinions, findings, and conclusions or recommendations expressed in this Report are those of the PI and do not necessarily reflect the views of the National Science Foundation; NSF has not approved or endorsed its content.
Modeling, analyzing, and visualizing information residing in complex datasets in actionable form are core problems in data science. This project addressed such problems in the realm of functional data, as they arise in multiple domains of science and application. The project aimed at developing mathematical methods and computational tools that help us to establish a pipeline from functional data to knowledge, as there is a vast landscape of potential uses for these methods in fields such as biology, ecology, medical imaging, and materials science.
Using mathematical formulations based on topology and geometry, the project developed methods and tools that can be used to summarize, analyze, and visualize functional data associated with complex shapes or networks. The project addressed theory, computation and applications. Through interdisciplinary collaboration with domain scientists and engineers, the methods were tested and validated in applications to the study of the phenotypic plasticity of plant leaves, the quantification of carbon nanotube alignment in materials with the aid of electron micrographs, as well as in analyses of medical images.
Other project activities included: (i) dissemination of research findings through publications in journals; (ii) presentations at conferences and workshops; (iii) education and training of students and postdoctoral scholars; (iv) participation in outreach activities for K-12 students.
Last Modified: 11/10/2021
Modified by: Washington Mio
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