Year: 2009
Author: James Lu
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 711–728
Abstract
This paper describes inverse eigenvalue problems that arise in studying qualitative dynamics in systems biology models. An algorithm based on lift-and-project iterations is proposed, where the lifting step entails solving a constrained matrix inverse eigenvalue problem. In particular, prior to carrying out the iterative steps, $a$-$priori$ bounds on the entries of the Jacobian matrix are computed by relying on the reaction network structure as well as the form of the rate law expressions for the model under consideration. Numerical results on a number of models show that the proposed algorithm can be used to computationally explore the possible dynamical scenarios while identifying the important mechanisms via the use of sparsity-promoting regularization.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/aamm.09-m09S04
Advances in Applied Mathematics and Mechanics, Vol. 1 (2009), Iss. 6 : pp. 711–728
Published online: 2009-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 18
Keywords: Inverse eigenvalue problems dynamical systems bifurcation biology sparsity.
Author Details
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