Volume 1, Issue 6
Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models

Adv. Appl. Math. Mech., 1 (2009), pp. 711-728.

Published online: 2009-01

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• 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.

• Keywords

Inverse eigenvalue problems, dynamical systems, bifurcation, biology, sparsity.

65F18, 93B55, 65P30, 37N25, 15A29

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@Article{AAMM-1-711, author = {}, title = {Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2009}, volume = {1}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.09-m09S04}, url = {http://global-sci.org/intro/article_detail/aamm/8393.html} }
TY - JOUR T1 - Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 711 EP - 728 PY - 2009 DA - 2009/01 SN - 1 DO - http://doi.org/10.4208/aamm.09-m09S04 UR - https://global-sci.org/intro/article_detail/aamm/8393.html KW - Inverse eigenvalue problems, dynamical systems, bifurcation, biology, sparsity. AB -

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.

James Lu. (1970). Inverse Eigenvalue Problems for Exploring the Dynamics of Systems Biology Models. Advances in Applied Mathematics and Mechanics. 1 (6). 711-728. doi:10.4208/aamm.09-m09S04
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