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A model for biological dynamic networks
1. | Department of Mathematical Sciences, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102, United States |
2. | Department of Mathematical Sciences and Center for Computational and Integrative Biology, Rutgers University - Camden, 311 N 5th Street, Camden, NJ 08102, United States |
References:
[1] |
U. Alon, "An Introduction to Systems Biology: Design Principles of Biological Circuits,", Chapman & Hall/CRC Mathematical and Computational Biology Series, (2007).
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[2] |
A.-L. Barabási and R. Albert, Emergence of scaling in random networks,, Science, 286 (1999), 509.
doi: 10.1126/science.286.5439.509. |
[3] |
A.-L. Barabási and R. E. Crandall, Linked: The new science of networks,, Am. J. Phys., 71 (2003), 409.
doi: 10.1119/1.1538577. |
[4] |
B. Bollobás, C. Borgs, J. Chayes and O. Riordan, Directed scale-free graphs,, in, (2003), 132.
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[5] |
M. Chaves and E. D. Sontag, State-estimation for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type,, Europ. J. of Control, 8 (2002), 343.
doi: 10.3166/ejc.8.343-359. |
[6] |
C. Cooper and A. Frieze, A general model of web graphs,, Random Struct. Alg., 22 (2003), 311.
doi: 10.1002/rsa.10084. |
[7] |
D. M. Cvetković, M. Doob and H. Sachs, "Spectra of Graphs: Theory and Applications,", Third edition, (1995).
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[8] |
D. Del Vecchio, A. J. Ninfa and E. D. Sontag, Modular cell biology: Retroactivity and insulation,, Mol. Syst. Biology, 4 (2008).
doi: 10.1038/msb4100204. |
[9] |
R. Durrett, "Random Graph Dynamics,", Cambridge Series in Statistical and Probabilistic Mathematics, (2007).
|
[10] |
P. Erdős and A. Renyi, On random graphs,, Publ. Math. Debrecen, 6 (1959), 290.
|
[11] |
M. Farina, R. Findeisen, E. Bullinger, S. Bittanti, F. Allgower and P. Wellstead, Results towards identifiability properties of biochemical reaction networks,, in, (2006), 13. Google Scholar |
[12] |
E. M. Hagos, Some results on graph spectra,, Linear Algebra Appl., 356 (2002), 103.
doi: 10.1016/S0024-3795(02)00324-5. |
[13] |
S. Mangan and U. Alon, Structure and function of the feed-forward loop network motif,, PNAS, 100 (2003), 11980.
doi: 10.1073/pnas.2133841100. |
[14] |
M. E. J. Newman, The structure and functions of complex networks,, SIAM Review, 45 (2003), 167.
doi: 10.1137/S003614450342480. |
[15] |
B. O. Palsson, "Systems Biology-Properties of Reconstructed Networks,", Cambridge University Press, (2006).
doi: 10.1017/CBO9780511790515. |
[16] |
E. D. Sontag, Molecular systems biology and control,, Europ. J. of Control, 11 (2005), 396.
|
[17] |
D. J. Watts and S. H. Strogatz, Collective dynamics of 'small-world' networks,, Nature, 393 (1998), 440.
doi: 10.1038/30918. |
show all references
References:
[1] |
U. Alon, "An Introduction to Systems Biology: Design Principles of Biological Circuits,", Chapman & Hall/CRC Mathematical and Computational Biology Series, (2007).
|
[2] |
A.-L. Barabási and R. Albert, Emergence of scaling in random networks,, Science, 286 (1999), 509.
doi: 10.1126/science.286.5439.509. |
[3] |
A.-L. Barabási and R. E. Crandall, Linked: The new science of networks,, Am. J. Phys., 71 (2003), 409.
doi: 10.1119/1.1538577. |
[4] |
B. Bollobás, C. Borgs, J. Chayes and O. Riordan, Directed scale-free graphs,, in, (2003), 132.
|
[5] |
M. Chaves and E. D. Sontag, State-estimation for chemical reaction networks of Feinberg-Horn-Jackson zero deficiency type,, Europ. J. of Control, 8 (2002), 343.
doi: 10.3166/ejc.8.343-359. |
[6] |
C. Cooper and A. Frieze, A general model of web graphs,, Random Struct. Alg., 22 (2003), 311.
doi: 10.1002/rsa.10084. |
[7] |
D. M. Cvetković, M. Doob and H. Sachs, "Spectra of Graphs: Theory and Applications,", Third edition, (1995).
|
[8] |
D. Del Vecchio, A. J. Ninfa and E. D. Sontag, Modular cell biology: Retroactivity and insulation,, Mol. Syst. Biology, 4 (2008).
doi: 10.1038/msb4100204. |
[9] |
R. Durrett, "Random Graph Dynamics,", Cambridge Series in Statistical and Probabilistic Mathematics, (2007).
|
[10] |
P. Erdős and A. Renyi, On random graphs,, Publ. Math. Debrecen, 6 (1959), 290.
|
[11] |
M. Farina, R. Findeisen, E. Bullinger, S. Bittanti, F. Allgower and P. Wellstead, Results towards identifiability properties of biochemical reaction networks,, in, (2006), 13. Google Scholar |
[12] |
E. M. Hagos, Some results on graph spectra,, Linear Algebra Appl., 356 (2002), 103.
doi: 10.1016/S0024-3795(02)00324-5. |
[13] |
S. Mangan and U. Alon, Structure and function of the feed-forward loop network motif,, PNAS, 100 (2003), 11980.
doi: 10.1073/pnas.2133841100. |
[14] |
M. E. J. Newman, The structure and functions of complex networks,, SIAM Review, 45 (2003), 167.
doi: 10.1137/S003614450342480. |
[15] |
B. O. Palsson, "Systems Biology-Properties of Reconstructed Networks,", Cambridge University Press, (2006).
doi: 10.1017/CBO9780511790515. |
[16] |
E. D. Sontag, Molecular systems biology and control,, Europ. J. of Control, 11 (2005), 396.
|
[17] |
D. J. Watts and S. H. Strogatz, Collective dynamics of 'small-world' networks,, Nature, 393 (1998), 440.
doi: 10.1038/30918. |
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