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Update sequence stability in graph dynamical systems
1. | Department of Mathematical Sciences, Clemson University, Clemson, SC 29634, United States |
2. | Department of Mathematics, NDSSL, Virginia Bioinformatics Institute, Virginia Tech, Blacksburg, VA 24061, United States |
References:
[1] |
C. L. Barrett, H. H. Hunt, M. V. Marathe, S. S. Ravi, D. Rosenkrantz, R. Stearns and P. Tosic, Gardens of Eden and fixed point in sequential dynamical systems, DM-CCG 2001, 95-110. |
[2] |
C. L. Barrett, H. S. Mortveit and C. M. Reidys, Elements of a theory of simulation III: Equivalence of SDS, Appl. Math. Comput., 122 (2001), 325-340.
doi: 10.1016/S0096-3003(00)00042-4. |
[3] |
C. L. Barrett, H. S. Mortveit and C. M. Reidys, Elements of a theory of simulation IV: Fixed points, invertibility and equivalence, Appl. Math. Comput., 134 (2003), 153-172.
doi: 10.1016/S0096-3003(01)00277-6. |
[4] |
C. L. Barrett, H. B. Hunt III, M. V. Marathe, S. S. Ravi, D. J. Rosenkrantz and R. E. Stearns, Predecessor and permutation existence problems for sequential dynamical systems, DMTCS 2003, 69-80. |
[5] |
A. Björner and F. Brenti, "Combinatorics of Coxeter Groups,'' Springer-Verlag, New York, 2005. |
[6] |
B. Bollobàs, "Random Graphs,'' Cambridge University Press, 2001. |
[7] |
R. Laubenbacher E. Sontag, A. Veliz-Cuba and A. Salam Jarrah, The effect of negative feedback loops on the dynamics of Boolean networks, Biophys. J., 95 (2008), 518-526.
doi: 10.1529/biophysj.107.125021. |
[8] |
D. L. Vertigan F. Jaeger and D. J. A. Welsh, On the computational complexity of the Jones and Tutte polynomials, Math. Proc. Cambridge Philos. Soc. 108 (1990), 35-53.
doi: 10.1017/S0305004100068936. |
[9] |
A. Å. Hansson, H. S. Mortveit and C. M. Reidys, On asynchronous cellular automata, Adv. Complex Systems, 8 (2005), no. 4, 521-538. |
[10] |
U. Karaoz, T. M. Murali, S. Letovsky, Y. Zheng, C. Ding, C. R. Cantor and S. Kasif, Whole-genome annotation by using evidence integration in functional-linkage networks, Proc. Nat. Acad. Sci., 101 (2004), 2888-2893.
doi: 10.1073/pnas.0307326101. |
[11] |
W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Royal Soc. London A, 115 (1927), 700-721.
doi: 10.1098/rspa.1927.0118. |
[12] |
V. S. A. Kumar, M. Macauley and H. S. Mortveit, Limit set reachability in asynchronous graph dynamical systems, RP 2009, 217-232. |
[13] |
M. Macauley, J. McCammond and H. S. Mortveit, Dynamics groups of asynchronous cellular automata, J. Algebraic Combinat, 33 (2011), 11-35.
doi: 10.1007/s10801-010-0231-y. |
[14] |
M. Macauley, J. McCammond and H. S. Mortveit, Order independence in asynchronous cellular automata, J. Cell. Autom., 3 (2008), 37-56. |
[15] |
M. Macauley and H. S. Mortveit, On enumeration of conjugacy classes of Coxeter elements, Proc. Amer. Math. Soc., 136 (2008), 4157-4165.
doi: 10.1090/S0002-9939-08-09543-9. |
[16] |
M. Macauley and H. S. Mortveit, Cycle equivalence of graph dynamical systems, Nonlinearity, 22 (2009), 421-436.
doi: 10.1088/0951-7715/22/2/010. |
[17] |
H. S. Mortveit and C. M. Reidys, "An Introduction to Sequential Dynamical Systems," Universitext, Springer Verlag, 2007. |
[18] |
C. M. Reidys, Sequential dynamical systems over words, Ann. Comb., 10 (2006), 481-498.
doi: 10.1007/s00026-006-0301-y. |
[19] |
C. M. Reidys, Combinatorics of sequential dynamical systems, Discrete Math., 308 (2007), 514-528.
doi: 10.1016/j.disc.2007.03.033. |
[20] |
I. Shmulevich, E. R. Dougherty and W. Zhang, From Boolean to probabilistic Boolean networks as models of genetic regulatory networks, Proc. IEEE, 90 (2002), 1778-1792.
doi: 10.1109/JPROC.2002.804686. |
[21] |
S. Wolfram, "Theory and Applications of Cellular Automata," Adv. Ser. Complex Systems, 1, World Scientific Publishing Company, 1986. |
show all references
References:
[1] |
C. L. Barrett, H. H. Hunt, M. V. Marathe, S. S. Ravi, D. Rosenkrantz, R. Stearns and P. Tosic, Gardens of Eden and fixed point in sequential dynamical systems, DM-CCG 2001, 95-110. |
[2] |
C. L. Barrett, H. S. Mortveit and C. M. Reidys, Elements of a theory of simulation III: Equivalence of SDS, Appl. Math. Comput., 122 (2001), 325-340.
doi: 10.1016/S0096-3003(00)00042-4. |
[3] |
C. L. Barrett, H. S. Mortveit and C. M. Reidys, Elements of a theory of simulation IV: Fixed points, invertibility and equivalence, Appl. Math. Comput., 134 (2003), 153-172.
doi: 10.1016/S0096-3003(01)00277-6. |
[4] |
C. L. Barrett, H. B. Hunt III, M. V. Marathe, S. S. Ravi, D. J. Rosenkrantz and R. E. Stearns, Predecessor and permutation existence problems for sequential dynamical systems, DMTCS 2003, 69-80. |
[5] |
A. Björner and F. Brenti, "Combinatorics of Coxeter Groups,'' Springer-Verlag, New York, 2005. |
[6] |
B. Bollobàs, "Random Graphs,'' Cambridge University Press, 2001. |
[7] |
R. Laubenbacher E. Sontag, A. Veliz-Cuba and A. Salam Jarrah, The effect of negative feedback loops on the dynamics of Boolean networks, Biophys. J., 95 (2008), 518-526.
doi: 10.1529/biophysj.107.125021. |
[8] |
D. L. Vertigan F. Jaeger and D. J. A. Welsh, On the computational complexity of the Jones and Tutte polynomials, Math. Proc. Cambridge Philos. Soc. 108 (1990), 35-53.
doi: 10.1017/S0305004100068936. |
[9] |
A. Å. Hansson, H. S. Mortveit and C. M. Reidys, On asynchronous cellular automata, Adv. Complex Systems, 8 (2005), no. 4, 521-538. |
[10] |
U. Karaoz, T. M. Murali, S. Letovsky, Y. Zheng, C. Ding, C. R. Cantor and S. Kasif, Whole-genome annotation by using evidence integration in functional-linkage networks, Proc. Nat. Acad. Sci., 101 (2004), 2888-2893.
doi: 10.1073/pnas.0307326101. |
[11] |
W. O. Kermack and A. G. McKendrick, A contribution to the mathematical theory of epidemics, Proc. Royal Soc. London A, 115 (1927), 700-721.
doi: 10.1098/rspa.1927.0118. |
[12] |
V. S. A. Kumar, M. Macauley and H. S. Mortveit, Limit set reachability in asynchronous graph dynamical systems, RP 2009, 217-232. |
[13] |
M. Macauley, J. McCammond and H. S. Mortveit, Dynamics groups of asynchronous cellular automata, J. Algebraic Combinat, 33 (2011), 11-35.
doi: 10.1007/s10801-010-0231-y. |
[14] |
M. Macauley, J. McCammond and H. S. Mortveit, Order independence in asynchronous cellular automata, J. Cell. Autom., 3 (2008), 37-56. |
[15] |
M. Macauley and H. S. Mortveit, On enumeration of conjugacy classes of Coxeter elements, Proc. Amer. Math. Soc., 136 (2008), 4157-4165.
doi: 10.1090/S0002-9939-08-09543-9. |
[16] |
M. Macauley and H. S. Mortveit, Cycle equivalence of graph dynamical systems, Nonlinearity, 22 (2009), 421-436.
doi: 10.1088/0951-7715/22/2/010. |
[17] |
H. S. Mortveit and C. M. Reidys, "An Introduction to Sequential Dynamical Systems," Universitext, Springer Verlag, 2007. |
[18] |
C. M. Reidys, Sequential dynamical systems over words, Ann. Comb., 10 (2006), 481-498.
doi: 10.1007/s00026-006-0301-y. |
[19] |
C. M. Reidys, Combinatorics of sequential dynamical systems, Discrete Math., 308 (2007), 514-528.
doi: 10.1016/j.disc.2007.03.033. |
[20] |
I. Shmulevich, E. R. Dougherty and W. Zhang, From Boolean to probabilistic Boolean networks as models of genetic regulatory networks, Proc. IEEE, 90 (2002), 1778-1792.
doi: 10.1109/JPROC.2002.804686. |
[21] |
S. Wolfram, "Theory and Applications of Cellular Automata," Adv. Ser. Complex Systems, 1, World Scientific Publishing Company, 1986. |
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