Symmetry in critical random Boolean network dynamics

Physical Review E - Statistical, Nonlinear, and Soft Matter Physics

Volumn 89, Issue 4, 2014, Pages

  Hossein, Shabnam ^a,b   Reichl, Matthew D ^a,b   Bassler, Kevin E ^a,b,c  

^a University of Houston   (United States)

^b UNIVERSITY OF HOUSTON   (United States)

^c MAX PLANCK INSTITUT FÜR PHYSIK KOMPLEXER SYSTEME   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN FUNCTIONS; CRITICAL CURRENT DENSITY (SUPERCONDUCTIVITY); ORDER DISORDER TRANSITIONS;

BOOLEAN NETWORKS; CRITICAL STATE; EVOLUTIONARY PROCESS; NETWORK DYNAMICS; NETWORK ROBUSTNESS; OUTPUT FUNCTIONS; RANDOM BOOLEAN NETWORKS; SYMMETRY GROUPS;

DYNAMICS;

EID: 84899749876     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.89.042808     Document Type: Article

References (58)

1. D. Griffiths, Elementary Particles (Wiley-VCH, Weinheim, 2005).
2. L. P. Kadanoff, Statistical Physics: Statics, Dynamics and Renormalization (World Scientific, Singapore, River Edge, NJ, 2000).
3. N. Boccara, Modeling Complex Systems (Springer, New York, 2010).
4. R. Albert and A.-L. Barabási, Rev. Mod. Phys. 74, 47 (2002). RMPHAT 0034-6861 10.1103/RevModPhys.74.47
5. K. Richter and J.-M. Rost, Komplexe Systeme (Fischer Taschenbuch Verlag, Frankfurt am Main, 2002).
6. G. Claudius, Complex and Adaptive Dynamical Systems a Primer (Springer, Berlin, 2008).
7. S. Boccaletti, V. Latora, Y. Moreno, M. Chavez, and D.-U. Hwang, Phys. Rep. 424, 175 (2006). PRPLCM 0370-1573 10.1016/j.physrep.2005.10.009 (Pubitemid 43135890)
8. B. Derrida and D. Stauffer, Europhys. Lett. 2, 739 (1986). EULEEJ 0295-5075 10.1209/0295-5075/2/10/001
9. S. Kauffman, Nature (London) 224, 177 (1969). NATUAS 0028-0836 10.1038/224177a0
10. R. Albert and H. G. Othmer, J. Theor. Biol. 223, 1 (2003). JTBIAP 0022-5193 10.1016/S0022-5193(03)00035-3 (Pubitemid 36627542)
11. C. Espinosa-Soto, P. Padilla-Longoria, and E. R. Alvarez-Buylla, Plant Cell Online 16, 2923 (2004). PLCEEW 1040-4651 10.1105/tpc.104.021725 (Pubitemid 41075743)
12. S. Pandey, R.-S. Wang, L. Wilson, S. Li, Z. Zhao, T. E. Gookin, S. M. Assmann, and R. Albert, Mol. Syst. Biol. 6 (2010). 1744-4292 10.1038/msb.2010.28
13. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, Proc. Natl. Acad. Sci. U.S.A. 101, 4781 (2004). PNASA6 0027-8424 10.1073/pnas.0305937101 (Pubitemid 38469154)
14. S. Bornholdt and T. Rohlf, Phys. Rev. Lett. 84, 6114 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.6114
15. L. P. Wang, E. E. Pichler, and J. Ross, Proc. Natl. Acad. Sci. 87, 9467 (1990). PNASA6 0027-8424 10.1073/pnas.87.23.9467
16. M. Aldana, S. Coppersmith, and L. P. Kadanoff, in Perspectives and Problems in Nolinear Science, edited by E. Kaplan, J. E. Marsden, and K. R. Sreenivasan (Springer, New York, 2003), pp. 23-89.
17. R.-S. Wang, A. Saadatpour, and R. Albert, Phys. Biol. 9, 055001 (2012). 1478-3967 10.1088/1478-3975/9/5/055001
18. S. Bornholdt, Science 310, 449 (2005). SCIEAS 0036-8075 10.1126/science.1119959 (Pubitemid 41507947)
19. M. A. Harrison, Introduction to Switching Theory and Automata, 1st ed. (McGraw-Hill, New York, 1965).
20. D. Green, T. Leishman, and S. Sadedin, in IEEE Symposium on Artificial Life, 2007. ALIFE '07 (IEEE, Honolulu, Hawaii, 2007), pp. 402-408.
21. X. Gong and J. E. S. Socolar, Phys. Rev. E 85, 066107 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.85.066107
22. U. Bastolla and G. Parisi, J. Theor. Biol. 187, 117 (1997). JTBIAP 0022-5193 10.1006/jtbi.1997.0423 (Pubitemid 27338672)
23. A. Bhattacharjya and S. Liang, Phys. Rev. Lett. 77, 1644 (1996). PRLTAO 0031-9007 10.1103/PhysRevLett.77.1644
24. J. M. Yeomans, Statistical Mechanics of Phase Transitions (Clarendon, Oxford University Press, Oxford, England, New York, 1992).
25. N. H. Packard, in Dynamic Patterns in Complex Systems, edited by J. A. S. Kelso, A. J. Mandell, and M. F. Shlesinger (World Scientic, Singapore, 1988), pp. 293-301.
26. B. Derrida and Y. Pomeau, Europhys. Lett. 1, 45 (1986). EULEEJ 0295-5075 10.1209/0295-5075/1/2/001
27. M. Paczuski, K. E. Bassler, and A. Corral, Phys. Rev. Lett. 84, 3185 (2000). PRLTAO 0031-9007 10.1103/PhysRevLett.84.3185
28. B. D. MacArthur, and R. J. Sánchez-García, Phys. Rev. E 80, 026117 (2009). PLEEE8 1539-3755 10.1103/PhysRevE.80.026117
29. S. A. Kauffman, The Origins of Order: Self-organization and Selection in Evolution (Oxford University Press, New York, 1993).
30. C. H. Waddington, Nature (London) 150, 563 (1942). NATUAS 0028-0836 10.1038/150563a0
31. M. Liu and K. E. Bassler, J. Phys. A: Math. Theor. 44, 045101 (2011). 1751-8113 10.1088/1751-8113/44/4/045101
32. C. C. Walker and W. R. Ashby, Kybernetik 3, 100 (1966). BICYAF 0340-1200 10.1007/BF00299903
33. U. Bastolla and G. Parisi, Physica D 115, 203 (1998). PDNPDT 0167-2789 10.1016/S0167-2789(97)00243-1
34. J. E. S. Socolar and S. A. Kauffman, Phys. Rev. Lett. 90, 068702 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.068702
35. V. Kaufman and B. Drossel, New J. Phys. 8, 228 (2006). NJOPFM 1367-2630 10.1088/1367-2630/8/10/228 (Pubitemid 44547586)
36. B. Samuelsson and J. E. S. Socolar, Phys. Rev. E 74, 036113 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.74.036113 (Pubitemid 44483517)
37. V. Kaufman, T. Mihaljev, and B. Drossel, Phys. Rev. E 72, 046124 (2005). PLEEE8 1539-3755 10.1103/PhysRevE.72.046124 (Pubitemid 41777934)
38. T. Mihaljev and B. Drossel, Phys. Rev. E 74, 046101 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.74.046101 (Pubitemid 44520431)
39. C. J. O. Reichhardt and K. E. Bassler, J. Phys. A: Math. Theor. 40, 4339 (2007). 1751-8113 10.1088/1751-8113/40/16/006
40. F. Schwabl, Statistical Mechanics (Springer, Berlin, New York, 2006).
41. B. Samuelsson and C. Troein, Phys. Rev. Lett. 90, 098701 (2003). PRLTAO 0031-9007 10.1103/PhysRevLett.90.098701
42. U. Bastolla and G. Parisi, Physica D 115, 219 (1998). PDNPDT 0167-2789 10.1016/S0167-2789(97)00242-X
43. S. Bilke and F. Sjunnesson, Phys. Rev. E 65, 016129 (2001). 1063-651X 10.1103/PhysRevE.65.016129
44. M. Möller and B. Drossel, New J. Phys. 14, 023051 (2012). NJOPFM 1367-2630 10.1088/1367-2630/14/2/023051
45. U. Paul, V. Kaufman, and B. Drossel, Phys. Rev. E 73, 026118 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.73.026118 (Pubitemid 43287707)
46. A. Wagner, Robustness and Evolvability in Living Systems (Princeton University Press, Princeton, N.J., Woodstock, 2007).
47. P. Bak and K. Sneppen, Phys. Rev. Lett. 71, 4083 (1993). PRLTAO 0031-9007 10.1103/PhysRevLett.71.4083
48. M. Paczuski, S. Maslov, and P. Bak, Phys. Rev. E 53, 414 (1996). 1063-651X 10.1103/PhysRevE.53.414
49. D. Challet and Y.-C. Zhang, Physica A 246, 407 (1997). PHYADX 0378-4371 10.1016/S0378-4371(97)00419-6
50. Y.-C. Zhang, Europhys. News 29, 51 (1998).
51. K. E. Bassler, C. Lee, and Y. Lee, Phys. Rev. Lett. 93, 038101 (2004). PRLTAO 0031-9007 10.1103/PhysRevLett.93.038101
52. M. D. Reichl and K. E. Bassler, Phys. Rev. E 84, 056103 (2011). PLEEE8 1539-3755 10.1103/PhysRevE.84.056103
53. T. Gross, C. J. Dommar D'Lima, and B. Blasius, Phys. Rev. Lett. 96, 208701 (2006). PRLTAO 0031-9007 10.1103/PhysRevLett.96.208701 (Pubitemid 43788422)
54. M. Hargittai, Symmetry Through the Eyes of a Chemist, 3rd ed. (Springer, Netherlands, 2009).
55. M. A. Harrison, J. Soc. Ind. Appl. Math. 11, 806 (1963). JSIMAV 0368-4245 10.1137/0111059
56. M. Rybarsch and S. Bornholdt, Phys. Rev. E 86, 026114 (2012). PLEEE8 1539-3755 10.1103/PhysRevE.86.026114
57. J. G. T. Zañudo, M. Aldana, and G. Martínez-Mekler, in Information Processing and Biological Systems, Intelligent Systems Reference Library No. 11, edited by S. Niiranen and A. Ribeiro (Springer, Berlin, Heidelberg, 2011), pp. 113-151.
58. M. Liu and K. E. Bassler, Phys. Rev. E 74, 041910 (2006). PLEEE8 1539-3755 10.1103/PhysRevE.74.041910 (Pubitemid 44600768)