| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | September 8, 2016 |
| Latest Amendment Date: | September 8, 2016 |
| Award Number: | 1620109 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Leland Jameson
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | September 1, 2016 |
| End Date: | August 31, 2019 (Estimated) |
| Total Intended Award Amount: | $133,547.00 |
| Total Awarded Amount to Date: | $133,547.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
210 N 4TH ST FL 4 SAN JOSE CA US 95112-5569 (408)924-1400 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
One Washington Square San Jose CA US 95192-0103 |
| 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): | COMPUTATIONAL MATHEMATICS |
| Primary Program Source: |
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| 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
This project is focused on applications of computational mathematics to problems arising in neuroscience and systems biology. Beyond utilizing currently available methods in creative ways, the main aim is to develop new computational methods to meet the needs of specific biological applications, particularly in systems biology and neuroscience. In systems biology, the goal is to understand complicated biological processes by studying interactions in a network setting rather than in isolation. While in neuroscience, the goal is to better understand neural connections in the brain, and how the brain interacts with it's external environment. On the systems biology side, the work in the proposed project will help make sense of two types of networks: biochemical reaction networks, deterministic models for molecular interactions, and protein-protein interaction networks, relational data collected, confirmed, and refined over the past decade. On the neuroscience side, the focus will be on neuronal networks, schematics that record connections between neurons, and combinatorial neural codes, a form of discretized cell firing data.
The techniques employed will come from combinatorics and computational algebraic geometry, two subfields with applications in an array of fields including statistics, physics, engineering, and biology. The proposal has three main research components. First, techniques and theory from computational algebraic geometry, such as toric ideals and Groebner bases, will be used to understand and visualize neuroscience data. Second, new algorithms for sampling random graphs with fixed properties will be developed for testing statistical hypotheses about protein-protein interaction and neuronal networks. Third, new algorithms for computing elimination ideals will be developed with the goal of applying these new methods to model selection in biochemical reaction network theory.
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.
This interdisciplinary project developed new tools in computational algebraic geometry and combinatorics for application in the biological sciences with a specific focus on neuroscience and systems biology. In particular, there were three main threads of the project: using computational algebraic geometry to understand neural codes arising in cognitive neuroscience, using algebraic statistics and graph sampling algorithms to develop statistical procedures for the analysis of neuronal networks and protein-protein interaction networks, and developing new combinatorial commutative algebra techniques for the use in parameter estimation and model selection of biochemical reaction networks.
In regards to neuroscience, this project developed novel techniques to take data and establish whether its possible that the data came from a collection of neurons that behave as place cells. In regards to systems biology, this project produced an foundational understanding of how model properties change as we build larger models from a collection of smaller motifs. The mathematical models studied in this project are used to understand diseases such as cancer, epidemics, and drug response. By understanding the theoretical underpinnings of these models, we can understand the full capability and limitations in these models, leading to better disease interventions and an overall improvement in public health.
Finally, this project also trained undergraduate and graduate students in research, directly impacting human resource development in the mathematical sciences.
Last Modified: 12/20/2019
Modified by: Elizabeth A Gross
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