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We revisit a model reductionmethod for detailed-balanced chemical reaction networks based on Kron reduction on the graph of complexes. The resulting reduced model preserves a number of important properties of the original model, such as, the kinetics law and identity of the chemical species. For determining the set of chemical complexes for the deletion, we propose two alternative methods to the computation of error integral which requires numerical integration of the state equations. The first one is based on the spectral clustering method and the second one is based on the eigenvalue interlacing property of Kron reduction on the graph. The efficacy of the proposed methods is evaluated on two biological models.

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Chicago
Jayawardhana, Bayu, Shodhan Rao, Ward Sikkema, and Barbara M Bakker. 2015. “Handling Biological Complexity Using Kron Reduction.” In Mathematical Control Theory I : Nonlinear and Hybrid Control Systems, ed. M Kanat Camlibel, A Agung Julius, Ramkrishna Pasumarthy, and Jacquelien MA Scherpen, 461:73–93. Cham, Switzerland: Springer.
APA
Jayawardhana, B., Rao, S., Sikkema, W., & Bakker, B. M. (2015). Handling biological complexity using Kron reduction. In M. K. Camlibel, A. A. Julius, R. Pasumarthy, & J. M. Scherpen (Eds.), Mathematical control theory I : nonlinear and hybrid control systems (Vol. 461, pp. 73–93). Cham, Switzerland: Springer.
Vancouver
1.
Jayawardhana B, Rao S, Sikkema W, Bakker BM. Handling biological complexity using Kron reduction. In: Camlibel MK, Julius AA, Pasumarthy R, Scherpen JM, editors. Mathematical control theory I : nonlinear and hybrid control systems. Cham, Switzerland: Springer; 2015. p. 73–93.
MLA
Jayawardhana, Bayu, Shodhan Rao, Ward Sikkema, et al. “Handling Biological Complexity Using Kron Reduction.” Mathematical Control Theory I : Nonlinear and Hybrid Control Systems. Ed. M Kanat Camlibel et al. Vol. 461. Cham, Switzerland: Springer, 2015. 73–93. Print.
@incollection{6988966,
  abstract     = {We revisit a model reductionmethod for detailed-balanced chemical reaction networks based on Kron reduction on the graph of complexes. The resulting reduced model preserves a number of important properties of the original model, such as, the kinetics law and identity of the chemical species. For determining the set of chemical complexes for the deletion, we propose two alternative methods to the computation of error integral which requires numerical integration of the state equations. The first one is based on the spectral clustering method and the second one is based on the eigenvalue interlacing property of Kron reduction on the graph. The efficacy of the proposed methods is evaluated on two biological models.},
  author       = {Jayawardhana, Bayu and Rao, Shodhan and Sikkema, Ward and Bakker, Barbara M},
  booktitle    = {Mathematical control theory I : nonlinear and hybrid control systems},
  editor       = {Camlibel, M Kanat and Julius, A Agung and Pasumarthy, Ramkrishna and Scherpen, Jacquelien MA},
  isbn         = {9783319209883},
  issn         = {0170-8643},
  language     = {eng},
  pages        = {73--93},
  publisher    = {Springer},
  series       = {Lecture Notes in Control and Information Sciences},
  title        = {Handling biological complexity using Kron reduction},
  url          = {http://dx.doi.org/10.1007/978-3-319-20988-3\_5},
  volume       = {461},
  year         = {2015},
}

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