Complex Systems with many interacting components can exhibit “Emergent Behaviour”, loosely characterised as something the individual components would not be expected to do on their own. In a recent paper [1] we identified “Strong Emergence” as behaviour which persists over time but is different for different repeats of the experiment. Persistent Mutual Information (PMI) was proposed as a way to detect and quantify this.

PMI is a simple extension of Gibbs Entropy, amounting to:
S(past) +S(future) – S(past and future taken together).

Further notes: pptx pdf

The aim of this project is to broaden the range of model examples studied (hitherto just the Logistic Map and the Standard Map), and thereby gain insight on how discriminating PMI can be. The work will involve both computer simulations of the models and/or extraction of time series from online sources, and numerical measurement of the PMI, the latter using either existing codes based on [2] or developing your own.

References:
[1] R. C. Ball, M. Diakonova, R. S. MacKay, “Quantifying Emergence in terms of Persistent Mutual Information”, Advances in Complex Systems, Vol. 13, No. 3 (2010) 327–338. arXiv:1003.3028v2
[2] Kraskov, A., Stogbauer, H., and Grassberger, P., Estimating mutual information,
Phys. Rev. E 69 (2004).

[ 3] Further notes - see links above in text.

Contact details:
Email: r.c.ball@warwick.ac.uk
Office: Room PS126