Information dynamics in small-world boolean networks

Artificial Life

Volumn 17, Issue 4, 2011, Pages 293-314

  Lizier, Joseph T ^a   Pritam, Siddharth ^a,b,c   Prokopenko, Mikhail Prokopenko ^a  

^a UNIVERSITY OF SYDNEY   (Australia)

^b CSIRO   (Australia)

^c MAX PLANCK INSTITUTE FOR MATHEMATICS IN THE SCIENCES   (Germany)

Author keywords

Distributed computation; Iinformation storage; Information transfer; Phase transitions; Random Boolean networks; Small world networks

Indexed keywords

DYNAMICS; PHASE TRANSITIONS; RANDOM PROCESSES; SMALL-WORLD NETWORKS; TOPOLOGY;

COMPUTATIONAL CAPABILITY; DISTRIBUTED COMPUTATIONS; INFORMATION DYNAMICS; INFORMATION TRANSFERS; NATURALLY OCCURRING NETWORKS; RANDOM BOOLEAN NETWORKS; TRANSFER CAPACITIES; TRANSFER INFORMATION;

DATA COMMUNICATION SYSTEMS;

ALGORITHM; ARTICLE; INFORMATION SCIENCE; THEORETICAL MODEL;

ALGORITHMS; INFORMATION THEORY; MODELS, THEORETICAL;

EID: 80053242464     PISSN: 10645462     EISSN: 15309185     Source Type: Journal    
DOI: 10.1162/artl_a_00040     Document Type: Article

References (55)

1. Aldana, M. (2003). Boolean dynamics of networks with scale-free topology. Physica D, 185, 45-66.
2. Amaral, L. A. N., Scala, A., Barthélémy, M., & Stanley, H. E. (2000). Classes of small-world networks. Proceedings of the National Academy of Sciences of the United States of America, 97, 11149-11152.
3. Argollo de Menezes, M., Moukarzel, C. F., & Penna, T. J. P. (2000). First-order transition in small-world networks. Europhysics Letters, 50, 574.
4. Atay, F. M., Jost, J., & Wende, A. (2004). Delays, connection topology, and synchronization of coupled chaotic maps. Physical Review Letters, 92, 144101.
5. Barabási, A.-L. (2009). Scale-free networks: A decade and beyond. Science, 325, 412-413.
6. Barthélémy, M., & Amaral, L. A. N. (1999). Small-world networks: Evidence for a crossover picture. Physical Review Letters, 82, 3180-3183. (Pubitemid 129689232)
7. Damiani, C., Kauffman, S., Serra, R., Villani, M., & Colacci, A. (2010). Information transfer among coupled random Boolean networks. In S. Bandini, S. Manzoni, H. Umeo, & G. Vizzari (Eds.), Cellular automata (pp. 1-11). Berlin: Springer.
8. Darabos, C., Giacobini, M., & Tomassini, M. (2007). Semi-synchronous activation in scale-free Boolean networks. In F. Almeida e Costa, L. M. Rocha, E. Costa, I. Harvey, & A. Coutinho (Eds.), Proceedings of the 9th European Conference on Artificial Life (ECAL 2007) (pp. 976-985). Berlin: Springer.
9. Derrida, B., & Pomeau, Y. (1986). Random networks of automata: A simple annealed approximation. Europhysics Letters, 1, 45-49.
10. Erdos, P., & Rényi, A. (1961). On the evolution of random graphs. Bulletin of the International Statistical Institute, 38, 343-347.
11. Feldman, D. P., & Crutchfield, J. P. (2003). Structural information in two-dimensional patterns: Entropy convergence and excess entropy. Physical Review E, 67, 051104.
12. Fisher, R. A. (1922). On the mathematical foundations of theoretical statistics. Philosophical Transactions of the Royal Society A, 220, 309-368.
13. Flyvbjerg, H. (1988). An order parameter for networks of automata. Journal of Physics A: Mathematical and General, 21, L955.
14. Gershenson, C. (2003). RBNLab. Online software: http://rbn.sourceforge. net.
15. Gershenson, C. (2004). Introduction to random Boolean networks. In M. Bedau, P. Husbands, T. Hutton, S. Kumar, & H. Suzuki (Eds.), Proceedings of the Workshops and Tutorials of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALife IX) (pp. 160-173).
16. Gershenson, C. (2004). Phase transitions in random Boolean networks with different updating schemes. ArXiv:nlin/0311008.
17. Gershenson, C. (2004). Updating schemes in random Boolean networks: Do they really matter? In J. Pollack, M. Bedau, P. Husbands, T. Ikegami, & R. A. Watson (Eds.), Proceedings of the Ninth International Conference on the Simulation and Synthesis of Living Systems (ALife IX) (pp. 238-243). Cambridge, MA: MIT Press.
18. Katare, S., & West, D. H. (2006). Optimal complex networks spontaneously emerge when information transfer is maximized at least expense: A design perspective. Nature Physics, 11, 26-35.
19. Kauffman, S. A. (1993). The origins of order: Self-organization and selection in evolution. Oxford, UK: Oxford University Press.
20. Kinouchi, O., & Copelli, M. (2006). Optimal dynamical range of excitable networks at criticality. Nature Physics, 2, 348-351.
21. Langton, C. G. (1990). Computation at the edge of chaos: Phase transitions and emergent computation. Physica D, 42, 12-37.
22. Latora, V., & Marchiori, M. (2001). Efficient behavior of small-world networks. Physical Review Letters, 87, 198701.
23. Lizier, J. T., Prokopenko, M., & Cornforth, D. J. (2009). The information dynamics of cascading failures in energy networks. In Proceedings of the European Conference on Complex Systems (ECCS) (p. 54).
24. Lizier, J. T., & Prokopenko, M. (2010). Differentiating information transfer and causal effect. European Physical Journal B, 73, 605-615.
25. Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (2007). Detecting non-trivial computation in complex dynamics. In F. Almeida e Costa, L. M. Rocha, E. Costa, I. Harvey, & A. Coutinho (Eds.), Proceedings of the 9th European Conference on Artificial Life (ECAL 2007) (pp. 895-904). Berlin: Springer.
26. Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (2008). The information dynamics of phase transitions in random Boolean networks. In S. Bullock, J. Noble, R. Watson, & M. A. Bedau (Eds.), Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems (ALife XI) (pp. 374-381). Cambridge, MA: MIT Press.
27. Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (2008). Local information transfer as a spatiotemporal filter for complex systems. Physical Review E, 77, 026110.
28. Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (2010). Information modification and particle collisions in distributed computation. Chaos, 20, 037109.
29. Lizier, J. T., Prokopenko, M., & Zomaya, A. Y. (in review). Local measures of information storage in complex distributed computation.
30. Lizier, J. T. (2010). The local information dynamics of distributed computation in complex systems. Ph.D. thesis, The University of Sydney.
31. Lu, Q., & Teuscher, C. (2009). Damage spreading in spatial and small-world random Boolean networks. arXiv:0904.4052.
32. Luque, B., Blanc, C., & Solé, R. V. (1997). Order parameters, Lyapunov exponents, and control in random Boolean networks (Working Paper 97-11-084). Santa Fe, NM: Santa Fe Institute.
33. MacKay, D. J. (2003). Information theory, inference, and learning algorithms. Cambridge, UK: Cambridge University Press.
34. Mitchell, M. (2006). Complex systems: Network thinking. Artificial Intelligence, 170, 1194-1212. (Pubitemid 44779546)
35. Newman, M., & Watts, D. J. (1999). Renormalization group analysis of the small-world network model. Physics Letters A, 263, 341-346.
36. Oosawa, C., & Savageau, M. A. (2002). Effects of alternative connectivity on behavior of randomly constructed Boolean networks. Physica D, 170, 143-161. (Pubitemid 34813926)
37. Rämö, P., Kauffman, S., Kesseli, J., & Yli-Harja, O. (2007). Measures for information propagation in Boolean networks. Physica D, 227, 100-104.
38. Ribeiro, A. S., Kauffman, S. A., Lloyd-Price, J., Samuelsson, B., & Socolar, J. E. S. (2008). Mutual information in random Boolean models of regulatory networks. Physical Review E, 77, 011901-10.
39. Rohlf, T., & Bornholdt, S. (2009). Self-organized criticality and adaptation in discrete dynamical networks. In T. Gross & H. Sayama (Eds.), Adaptive networks-Theory, models and applications (pp. 73-108). Berlin: Springer.
40. Rohlf, T., Gulbahce, N., & Teuscher, C. (2007). Damage spreading and criticality in finite random dynamical networks. Physical Review Letters, 99, 248701.
41. Schreiber, T. (2000). Measuring information transfer. Physical Review Letters, 85, 461-464.
42. Solé, R. V., & Valverde, S. (2001). Information transfer and phase transitions in a model of Internet traffic. Physica A, 289, 595-605. (Pubitemid 32092317)
43. Sporns, O., Rubinov, M., & Kötter, R. (2009). Brain connectivity toolbox. Online software: http://www.brain-connectivity-toolbox.net/.
44. Stauffer, D. (1989). Hunting for the fractal dimension of the Kauffman model. Physica D: Nonlinear Phenomena, 38, 341-344.
45. Stauffer, D. (1994). Evolution by damage spreading in Kauffman model. Journal of Statistical Physics, 74, 1293-1299.
46. Tassier, T., & Menczer, F. (2001). Emerging small-world referral networks in evolutionary labor markets. IEEE Transactions on Evolutionary Computation, 5, 482-492. (Pubitemid 33047924)
47. Teuscher, C. (2006). On irregular interconnect fabrics for self-assembled nanoscale electronics. In Proceedings of the 2nd IEEE International Workshop on Default and Fault Tolerant Nanoscale Architectures, NANOARCH'06 (pp. 60-67).
48. Tomassini, M., Giacobini, M., & Darabos, C. (2005). Evolution and dynamics of small-world cellular automata. Complex Systems, 15, 261-284. (Pubitemid 41643487)
49. Wang, X. R., Lizier, J. T., & Prokopenko, M. (2010). A Fisher information study of phase transitions in random Boolean networks. In H. Fellermann, M. Dörr, M. M. Hanczyc, L. L. Laursen, S. Maurer, D. Merkle, P.-A. Monnard, K. Stoy, & S. Rasmussen (Eds.), Proceedings of the 12th International Conference on the Synthesis and Simulation of Living Systems (Alife XII) (pp. 305-312). Cambridge, MA: MIT Press.
50. Wang, X. R., Lizier, J. T., & Prokopenko, M. (2011). Fisher information at the edge of chaos in random Boolean networks. Artificial Life, 17(4), 315-329.
51. Watts, D. J., & Strogatz, S. (1998). Collective dynamics of "small-world" networks. Nature, 393, 440-442.
52. Wuensche, A. (1997). Attractor basins of discrete networks. Ph.D. thesis, The University of Sussex.
53. Wuensche, A. (1999). Classifying cellular automata automatically: Finding gliders, filtering, and relating space-time patterns, attractor basins, and the Z parameter. Complexity, 4, 47-66. (Pubitemid 129180503)
54. Yuan, W.-J., Luo, X.-S., Jiang, P.-Q., Wang, B.-H., & Fang, J.-Q. (2008). Transition to chaos in small-world dynamical network. Chaos, Solitons & Fractals, 37, 799-806. (Pubitemid 351335367)
55. Zhang, X., & Zhao, Q. (2009). Effects of small world topology on the critical boundary for Boolean networks. Physica A, 388, 3657-3666.