| NSF Org: |
DMS Division Of Mathematical Sciences |
| Recipient: |
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| Initial Amendment Date: | July 22, 1999 |
| Latest Amendment Date: | July 22, 1999 |
| Award Number: | 9971852 |
| Award Instrument: | Standard Grant |
| Program Manager: |
Deborah Lockhart
DMS Division Of Mathematical Sciences MPS Directorate for Mathematical and Physical Sciences |
| Start Date: | August 1, 1999 |
| End Date: | July 31, 2002 (Estimated) |
| Total Intended Award Amount: | $105,000.00 |
| Total Awarded Amount to Date: | $105,000.00 |
| Funds Obligated to Date: |
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| History of Investigator: |
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| Recipient Sponsored Research Office: |
4333 BROOKLYN AVE NE SEATTLE WA US 98195-1016 (206)543-4043 |
| Sponsor Congressional District: |
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| Primary Place of Performance: |
4333 BROOKLYN AVE NE SEATTLE WA US 98195-1016 |
| 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): | APPLIED 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
9971852
Burke
Two topics are proposed for study: (1) the variational analysis of
eigenvalue functions and (2) non-parametric population analysis. In the
first topic the principal investigator will apply modern techniques of
nonsmooth analysis and variational geometry to study the variational
properties of certain functions of the spectrum on the space of n x n
complex valued matrices, e.g., the spectral abscissa and the spectral
radius. In the second topic, the principal investigator intends to analyze
and develop algorithmic solution techniques for the non-parametric
version of the basic problem of population analysis. Specifically, the
principal investigator intends to use maximum likelihood techniques to
estimate the underlying probability measure associated with population
variability.
Understanding the variational behavior of the spectrum of matrix valued
mappings is essential to our understanding and control of discrete and
continuous dynamical systems. Such systems arise in numerous practical
applications ranging from the design of structures that can withstand a
major earthquake to flight control for modern aircraft. The results of the
principal investigator's research program are intended to make possible for
the first time the derivation of optimality and/or equilibrium conditions for
numerous problems associated with spectral variations that occur in
numerous engineering applications. On the other hand, population analysis
is the statistical methodology used to understand inter-subject variability
in studies designed to analyze a phenomenon associated with a targeted
population. For example, the methodology is widely used in
pharmocokinetic studies since it is the key to understanding how drugs
behave in humans and animals. The principal investigator intends to
analyze and develop algorithmic solution techniques for the non-
parametric version of this problem. The goal is to incorporate these
algorithms into a software package now being developed by the Resource
Facility for Population Kinetics at the University of Washington.
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