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## The information dynamics of phase transitions in random boolean networks (2008)

Venue: | Proceedings of the Eleventh International Conference on the Simulation and Synthesis of Living Systems (ALife XI |

Citations: | 23 - 10 self |

### Citations

1936 | Information Theory, Inference & Learning Algorithms - MacKay - 2002 |

1682 |
The Origins of Order: Self-Organization and Selection in Evolution.NewYork:OxfordUniversityPress,
- Kauffman
- 1993
(Show Context)
Citation Context ...he element’s output, and inferring a maximization of information processing at criticality. We are particularly interested in investigating the information dynamics of Random Boolean Networks (RBNs) (=-=Kauffman, 1993-=-), in part because of the power in their generality as discrete dynamical network models with a large sample space available. Also, they have a well-known phase transition from ordered to chaotic dyna... |

253 |
Computation at the edge of chaos: Phase transitions and emergent computation.
- Langton
- 1990
(Show Context)
Citation Context ...elatively high connectivity and activity, the network is in a chaotic phase, characterized by low stability of states and divergence of similar macro states. In the critical phase (the edge of chaos (=-=Langton, 1990-=-)), there is percolation in nodes remaining static or updating their values, and uncertainty in the convergence or divergence of similar macro states. This phase transition is typically quantified usi... |

120 | Random networks of automata: a simple annealed approximation,”
- Derrida, Pomeau
- 1986
(Show Context)
Citation Context ..., B)t=0 = 1/N). Finding δ < 0, implies the convergence of similar initial states, while δ > 0 implies their divergence. For fixed p, the critical value of K between the ordered and chaotic phases is (=-=Derrida and Pomeau, 1986-=-): Kc = 1 . (3) 2p(1 − p) 1 There has been some debate about the best updating scheme to model GRNs (Darabos et al., 2007), and variations on the synchronous CRBN model are known to produce different ... |

73 |
Boolean dynamics of networks with scale-free topology.
- Aldana
- 2003
(Show Context)
Citation Context ...ransfer in cellular automata (Lizier et al., 2008b, 2007). We believe that information dynamics are particularly relevant to networked systems: while network’s structure has attracted much attention (=-=Aldana, 2003-=-), their time-series dynamics are “much less well understood” (Mitchell, 2006). Although the time-series dynamics of state-space trajectories and damage spreading are established, Mitchell (2006) sugg... |

70 | Introduction to Random Boolean Networks,
- Gershenson
- 2004
(Show Context)
Citation Context ... one, underlined by the comments of Mitchell (2006) on information dynamics in networks, and by the general importance attributed to information processing in biological systems (Polani et al., 2007; =-=Gershenson, 2004-=-a). Importantly, the perspective of distributed computation is unique in quantitatively aligning with our understanding of information storage, transfer and modification (Lizier et al., 2007). We begi... |

70 | Optimal dynamical range of excitable networks at criticality. - Kinouchi, Copelli - 2006 |

34 | Complex systems: Network thinking
- Mitchell
(Show Context)
Citation Context ...information dynamics are particularly relevant to networked systems: while network’s structure has attracted much attention (Aldana, 2003), their time-series dynamics are “much less well understood” (=-=Mitchell, 2006-=-). Although the time-series dynamics of state-space trajectories and damage spreading are established, Mitchell (2006) suggests that “the main challenge is understanding the dynamics of the propagatio... |

33 | Local information transfer as a spatiotemporal filter for complex systems.
- Lizier, Prokopenko, et al.
- 2008
(Show Context)
Citation Context ...e undertaking. Introduction The information dynamics of distributed computation has recently emerged as an important tool for studying complex systems, e.g. information transfer in cellular automata (=-=Lizier et al., 2008-=-b, 2007). We believe that information dynamics are particularly relevant to networked systems: while network’s structure has attracted much attention (Aldana, 2003), their time-series dynamics are “mu... |

28 | Tracking information flow through the environment: Simple cases of stigmergy.
- Klyubin, Polani, et al.
- 2004
(Show Context)
Citation Context ...o look for a framework to describe the information dynamics in complex systems, and indeed information theory is proving to be a useful framework for the analysis and design of complex systems, e.g. (=-=Klyubin et al., 2004-=-). The fundamental quantity is the (Shannon) entropy, which represents the uncertainty in a sample x of a random variable X: HX = − ∑ x p(x) log 2 p(x) (all with units in bits). The joint entropy of t... |

20 | The local information dynamics of distributed computation
- Lizier
- 2013
(Show Context)
Citation Context ...e undertaking. Introduction The information dynamics of distributed computation has recently emerged as an important tool for studying complex systems, e.g. information transfer in cellular automata (=-=Lizier et al., 2008-=-b, 2007). We believe that information dynamics are particularly relevant to networked systems: while network’s structure has attracted much attention (Aldana, 2003), their time-series dynamics are “mu... |

19 |
Structural information in two-dimensional patterns: Entropy convergence and excess entropy, Phys
- Crutchfield, Feldman
(Show Context)
Citation Context ... The information storage of an agent in the system is the amount of information in its past that is relevant to predicting its future. The excess entropy is the total information stored by the agent (=-=Feldman and Crutchfield, 2003-=-), while the active information storage is the stored information that is currently in use in computing the next state of the agent (Lizier et al., 2007). We focus on the active information since it y... |

17 | Detecting Non-trivial Computation in Complex Dynamics.
- Lizier, Prokopenko, et al.
- 2007
(Show Context)
Citation Context ... characterize the information dynamics of the distributed computation in terms of the elements of Turing universal computation: information storage, information transfer and information modification (=-=Lizier et al., 2007-=-). Our perspective of computation in RBNs is an important one, underlined by the comments of Mitchell (2006) on information dynamics in networks, and by the general importance attributed to informatio... |

14 | Updating schemes in random Boolean networks: Do they really matter - Gershenson - 2004 |

7 | Phase transitions in random Boolean networks with different updating schemes
- Gershenson
- 2004
(Show Context)
Citation Context ... one, underlined by the comments of Mitchell (2006) on information dynamics in networks, and by the general importance attributed to information processing in biological systems (Polani et al., 2007; =-=Gershenson, 2004-=-a). Importantly, the perspective of distributed computation is unique in quantitatively aligning with our understanding of information storage, transfer and modification (Lizier et al., 2007). We begi... |

4 |
Semisynchronous activation in scale-free boolean networks
- Darabos, Giacobini, et al.
- 2007
(Show Context)
Citation Context ...ixed p, the critical value of K between the ordered and chaotic phases is (Derrida and Pomeau, 1986): Kc = 1 . (3) 2p(1 − p) 1 There has been some debate about the best updating scheme to model GRNs (=-=Darabos et al., 2007-=-), and variations on the synchronous CRBN model are known to produce different behaviors. However, the relevant phase transitions are known to exist in all updating schemes, and their properties depen... |

1 | Revisiting the edge of chaos:evolving cellular automata to perform computations - Mitchell, Hraber, et al. - 1993 |