| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | July 19, 2013 |
| Latest Amendment Date: | July 19, 2013 |
| Award Number: | 1308899 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Tomek Bartoszynski
tbartosz@nsf.gov (703)292-4885 DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 1, 2013 |
| End Date: | July 31, 2016 (Estimated) |
| Total Intended Award Amount: | $130,350.00 |
| Total Awarded Amount to Date: | $130,350.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
3 RUTGERS PLZ NEW BRUNSWICK NJ US 08901-8559 (848)932-0150 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
NJ US 08901-8559 |
| 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): | PROBABILITY |
| Primary Program Source: |
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| Program Reference Code(s): | |
| Program Element Code(s): |
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| Award Agency Code: | 4900 |
| Fund Agency Code: | 4900 |
| Assistance Listing Number(s): | 47.049 |
ABSTRACT
The project studies probability models for evolving combinatorial structures, particularly partition, tree and graph-valued stochastic processes. Specific topics to be studied include representation and characterization theorems of combinatorial Markov processes, continuum tree and interval graph scaling limits, consistent systems of partition, tree and graph-valued processes, and connections to random matrices and Levy processes. The dominant theme of the research will be the effect of probabilistic symmetries, especially exchangeability, on the structural properties of evolving large combinatorial objects, as these structural properties impact various practical aspects of these processes.
As a result of this project, we should gain further understanding of models for time-varying discrete structures, especially partitions, trees and networks. Such processes arise as natural models in various disciplines, including genetics, physics, biology, computer science and statistics. In particular, understanding graph-valued processes has potentially far-reaching applications in the diverse and burgeoning field of complex networks. Effective models for real-world networks are relevant to problems in national security, public health, sociology, computer science and physical sciences. Other areas in which combinatorial models can be useful include phylogenetics, machine learning, statistics and Bayesian inference.
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.
Harry Crane has completed the research proposed under the project "Evolving Combinatorial Structures" funded from July 2013 to July 2016. The proposed project had several interdisciplinary goals regarding the study of mathematical structures that arise in applications in statistics, genetics, physics, social sciences, and national defense. As explained below, the project met and exceeded all project objectives.
The primary goal of the project was to develop sensible probabilistic models for modeling structures, e.g., partitions, trees, and graphs, that arise in scientific applications, e.g., clustering, phylogenetics, and networks, respectively. The main outcomes give a broad mathematical analysis of these processes as well as demonstrates their use on statistical applications.
The mathematical developments, in particular, look into statistical models for complex data structures that vary over time. In this work, the PI identifies a large class of models with suitable properties for practical implementation. The PI establishes ample mathematical properties of importance for statistical applications involving these processes.
The PI has demonstrated the practical use of the above methods with substantive work on theory and methods for clustering and network analysis. The PI demonstrates these methods to be more effective than competing approaches for their intended applications. The approaches also tend to be more computationally efficient.
Last Modified: 10/30/2016
Modified by: Harry Crane
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