Boolean networks with reliable dynamics

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

Volumn 80, Issue 5, 2009, Pages

  Peixoto, Tiago P ^a   Drossel, Barbara ^a  

^a DARMSTADT UNIVERSITY OF TECHNOLOGY   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

BOOLEAN NETWORKS; CLUSTERING COEFFICIENT; FIXED POINTS; GENE REGULATION NETWORK; HOMOGENEOUS FUNCTIONS; RANDOM NETWORK; STATE SPACE; STATE SPACE STRUCTURES;

SPACE PLATFORMS;

PROBABILITY DISTRIBUTIONS;

EID: 70449633301     PISSN: 15393755     EISSN: 15502376     Source Type: Journal    
DOI: 10.1103/PhysRevE.80.056102     Document Type: Article

References (19)

1. M. Rosen-Zvi, A. Engel, and I. Kanter, Phys. Rev. Lett. 87, 078101 (2001). 10.1103/PhysRevLett.87.078101
2. A. A. Moreira, A. Mathur, D. Diermeier, and L. A. N. Amaral, Proc. Natl. Acad. Sci. U.S.A. 101, 12085 (2004). 10.1073/pnas.0400672101
3. M. C. Lagomarsino, P. Jona, and B. Bassetti, Phys. Rev. Lett. 95, 158701 (2005). 10.1103/PhysRevLett.95.158701
4. S. Wolfram, A New Kind of Science (Wolfram Media, Champaign, IL, 2002).
5. S. A. Kauffman, J. Theor. Biol. 22, 437 (1969). 10.1016/0022-5193(69) 90015-0
6. B. Drossel, in Reviews of Nonlinear Dynamics and Complexity, edited by, H. G. Schuster, (Wiley, New York, 2008), Vol. 1.
7. F. Greil and B. Drossel, Phys. Rev. Lett. 95, 048701 (2005). 10.1103/PhysRevLett.95.048701
8. K. Klemm and S. Bornholdt, Phys. Rev. E 72, 055101 (R) (2005). 10.1103/PhysRevE.72.055101
9. F. Li, T. Long, Y. Lu, Q. Ouyang, and C. Tang, Proc. Natl. Acad. Sci. U.S.A. 101, 4781 (2004). 10.1073/pnas.0305937101
10. J. Aracena, E. Goles, A. Moreira, and L. Salinas, BioSystems 97, 1 (2009). 10.1016/j.biosystems.2009.03.006
11. K. Y. Lau, S. Ganguli, and C. Tang, Phys. Rev. E 75, 051907 (2007). 10.1103/PhysRevE.75.051907
12. M. E. J. Newman, SIAM Rev. 45, 167 (2003). 10.1137/S003614450342480
13. U. Alon, An Introduction to Systems Biology: Design Principles of Biological Circuits (Chapman & Hall, London/ CRC, London, 2007).
14. K. Klemm and S. Bornholdt, Proc. Natl. Acad. Sci. U.S.A. 102, 18414 (2005). 10.1073/pnas.0509132102
15. R. Milo, S. Itzkovitz, N. Kashtan, R. Levitt, S. Shen-Orr, I. Ayzenshtat, M. Sheffer, and U. Alon, Science 303, 1538 (2004). 10.1126/science.1089167
16. C. Gershenson, S. A. Kauffman, and I. Shmulevich, in Artificial Life X, Proceedings of the Tenth International Conference on the Simulation and Synthesis of Living Systems, edited by, L. S. Yaeger, M. A. Bedau, D. Floreano, R. L. Goldstone and, A. Vespignani, (MIT Press, Cambridge, MA, 2006), pp. 35-42.
17. D. E. Knuth, The Art of Computer Programming, Fascicle 3: Generating All Combinations and Partitions Vol. 4 (Addison-Wesley, Reading, MA, 2005).
18. Unlike in some types of graphs, those trajectories are always possible on hypercubes and are known as Grey codes in computer science.
19. We note that an alternative procedure that starts with an input set that contains all nodes and then randomly removes inputs, until a removal is no longer possible, is for larger k much faster than the procedure used by us. However, it will in general not produce a minimal network. As an example, consider the case where only one minimal set of k inputs is possible for a given node. In this case, if one of these inputs is removed early in the iteration, the input set obtained at the end will have a size larger than the minimal k.