Journal of applied mathematics & informatics

한국전산응용수학회 (The Korean Society for Computational and Applied Mathematics)
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A GRAPHICAL ALGORITHM FOR CALCULATING THE RANKS OF COMPLEX REACTION NETWORKS

  • Choo, S.M. (Department of Mathematics, University of Ulsan) ;
  • Lee, N.Y. (Department of Mathematics and Statistics, Minnesota State University)
  • 투고 : 2012.04.25
  • 심사 : 2012.06.30
  • 발행 : 2012.09.30
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초록

We present a graphical algorithm and theorems for calculating the ranks of reaction networks. The ranks are needed to study behaviors of the networks from their structures. This approach can graphically simplify complex networks for the calculation. We show an example of a large network for the practical advantage.

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과제정보

연구 과제 주관 기관 : University of Ulsan

참고문헌

  1. M. Banaji, P. Donnell, S. Baigent, P matrix properties, injectivity, and stability in chemical reaction systems, SIAM J. Appl. Math. 67 (2007), 1523-1547. https://doi.org/10.1137/060673412
  2. S.M. Choo, N.Y. Lee, New criteria for the existence of a positive equilibrium in reaction networks, App. Math. Lett. 24 (2011), 450-453. https://doi.org/10.1016/j.aml.2010.10.040
  3. G. Craciun, M. Feinberg, Multiple equilibria in complex chemical reaction networks: II. The Species- Reaction graph, SIAM J. Appl. Math. 66 (2006), 1321-1338. https://doi.org/10.1137/050634177
  4. S.Y. Shin, O. Rath, S.M. Choo, F. Fee, B. McFerran, W. Kolch, K.H. Cho, Functional roles of multiple feedback loops in extracellular signal-regulated kinase and Wnt signaling pathways that regulate epithelial-mesenchymal transition, Caner Res. 70 (2010), 6715-6724. https://doi.org/10.1158/0008-5472.CAN-10-1377