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Information Dynamics in Networks and Phase Transitions

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The Local Information Dynamics of Distributed Computation in Complex Systems

Part of the book series: Springer Theses ((Springer Theses))

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Abstract

As outlined in Sect. 2.4 the topology of networks has attracted much recent attention, however their time-series dynamics remains relatively poorly understood. In particular, the importance of quantitatively establishing the nature of distributed computation in networks is widely acknowledged, e.g. Mitchell [2] states “the main challenge is understanding the dynamics of the propagation of information ... in networks, and how these networks process such information.”

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Notes

  1. 1.

    This is commonly observed in such ensemble studies [17, 19].

  2. 2.

    See also the see sharpening of phase transition with system size for RBNs in [7, 20] and for another network type in [3].

  3. 3.

    Our information dynamics analysis of RBNs was first reported in [21], and the analysis of cascading failures first reported in [22].

  4. 4.

    This is unlike the mutual information measurements by Ribeiro et al. [7] and Solé and Valverde [3] for random node pairs (regardless of whether they are directly causally linked).

  5. 5.

    In contrast, this could be done for the homogeneous agents in CAs in the preceding chapters.

  6. 6.

    \(\delta \) was confirmed to change sign close to \(\overline{K} = 2\) here (as per [20]), with a subsequent slow increase after \(\overline{K} = 2\) (known to be a finite-\(N\) effect). The standard deviation of \(\delta \) is maximised during this increase in the chaotic regime [20]. Certain other measures suggested to indicate the critical phase are known to be shifted into the chaotic regime for finite-\(N\), e.g. [7]. Given impetus as an indicator of the critical phase by the related measure of Rämö et al. [6], we use the standard deviation of \(\delta \) as guide to the relative regions of dynamics in finite-\(N\) networks.

  7. 7.

    We have slightly altered the definition in [26], since this definition was ambiguous.

  8. 8.

    It could also be said that there is a large amount of assortative noise between the source and destination [3, 44].

  9. 9.

    We have since made this exploration of small-world Boolean networks in [49].

  10. 10.

    Note however that applying the framework to acyclic or feed-forward models such as [29, 45, 54, 55] (which are widely available since they are much simpler to infer) will reveal little more than trivial computation. This is because in the absence of external stimuli, acyclic models reach an attractor state very quickly, and the computation of the network is then completed.

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  1. CSIRO ICT Centre, Corner of Vimiera and Pembroke Rd, Marsfield, 2122, Australia

    Joseph T. Lizier

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Lizier, J.T. (2013). Information Dynamics in Networks and Phase Transitions. In: The Local Information Dynamics of Distributed Computation in Complex Systems. Springer Theses. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-32952-4_6

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