Generalized sensitivity functions for size-structured population models
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Dustin D. Keck
and David M. Bortz
Abstract
Size-structured population models provide a popular means to mathematically describe phenomena such as bacterial aggregation, schooling fish, and planetesimal evolution. For parameter estimation, a generalized sensitivity function (GSF) provides a tool that quantifies the impact of data from specific regions of the experimental domain. This function helps to identify the most relevant data subdomains, which enhances the optimization of experimental design. To our knowledge, GSFs have not been used in the partial differential equation (PDE) realm, so we provide a novel PDE extension of the discrete and continuous ordinary differential equation (ODE) concepts of Thomaseth and Cobelli and Banks et al. respectively. We analyze a GSF in the context of size-structured population models, and specifically analyze the Smoluchowski coagulation equation to determine the most relevant time and volume domains for three, distinct aggregation kernels. Finally, we provide evidence that parameter estimation for the Smoluchowski coagulation equation does not require post-gelation data.
Funding source: National Science Foundation
Award Identifier / Grant number: DMS-1225878
Funding statement: This work was supported in part by the National Science Foundation grant DMS-1225878.
We would like to thank Dr. John Younger in the Department of Emergency Medicine at the University of Michigan for discussions concerning experimental data. We would also like to acknowledge the anonymous reviewers who made several suggestions that greatly improved the clarity of this article.
© 2016 by De Gruyter
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Articles in the same Issue
- Frontmatter
- Inverse scattering problem for the nonstationary Dirac equation on the half-plane
- A Radon-type transform arising in photoacoustic tomography with circular detectors
- Recovery of the matrix quadratic differential pencil from the spectral data
- The effect of resonance on the linear sampling method
- Inverse problems for parabolic equations with interior degeneracy and Neumann boundary conditions
- Incorporating a posteriori error estimators in an adaptive parametrization algorithm
- Generalized sensitivity functions for size-structured population models
- Stable gradient projection method for nonlinear conditionally well-posed inverse problems
- Uniqueness and non-uniqueness in acoustic tomography of moving fluid
- Convex Tikhonov regularization in Banach spaces: New results on convergence rates
- Calderón problem for Maxwell's equations in two dimensions