Joseph T Lizier

Publications (26) View all

• Article: Identifying influential spreaders and efficiently estimating infection numbers in epidemic models: a walk counting approach

  Frank Bauer, Joseph T. Lizier
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  ABSTRACT: We introduce a new method to efficiently approximate the number of infections resulting from a given initially-infected node in a network of susceptible individuals. Our approach is based on counting the number of possible infection walks of various lengths to each other node in the network. We analytically study the properties of our method, in particular demonstrating different forms for SIS and SIR disease spreading (e.g. under the SIR model our method counts self-avoiding walks). In comparison to existing methods to infer the spreading efficiency of different nodes in the network (based on degree, k-shell decomposition analysis and different centrality measures), our method directly considers the spreading process and, as such, is unique in providing estimation of actual numbers of infections. Crucially, in simulating infections on various real-world networks with the SIR model, we show that our walks-based method improves the inference of effectiveness of nodes over a wide range of infection rates compared to existing methods. We also analyse the trade-off between estimate accuracy and computational cost, showing that the better accuracy here can still be obtained at a comparable computational cost to other methods.
  03/2012;
• Source

  Available from: Joschka Boedecker

  Article: Information processing in echo state networks at the edge of chaos.

  Joschka Boedecker, Oliver Obst, Joseph T Lizier, N Michael Mayer, Minoru Asada
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  ABSTRACT: We investigate information processing in randomly connected recurrent neural networks. It has been shown previously that the computational capabilities of these networks are maximized when the recurrent layer is close to the border between a stable and an unstable dynamics regime, the so called edge of chaos. The reasons, however, for this maximized performance are not completely understood. We adopt an information-theoretical framework and are for the first time able to quantify the computational capabilities between elements of these networks directly as they undergo the phase transition to chaos. Specifically, we present evidence that both information transfer and storage in the recurrent layer are maximized close to this phase transition, providing an explanation for why guiding the recurrent layer toward the edge of chaos is computationally useful. As a consequence, our study suggests self-organized ways of improving performance in recurrent neural networks, driven by input data. Moreover, the networks we study share important features with biological systems such as feedback connections and online computation on input streams. A key example is the cerebral cortex, which was shown to also operate close to the edge of chaos. Consequently, the behavior of model systems as studied here is likely to shed light on reasons why biological systems are tuned into this specific regime.
  Theory in Biosciences 12/2011; 131(3):205-13. · 0.98 Impact Factor
• Source

  Available from: lizier.me

  Article: Coherent information structure in complex computation.

  Joseph T Lizier, Mikhail Prokopenko, Albert Y Zomaya
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  ABSTRACT: We have recently presented a framework for the information dynamics of distributed computation that locally identifies the component operations of information storage, transfer, and modification. We have observed that while these component operations exist to some extent in all types of computation, complex computation is distinguished in having coherent structure in its local information dynamics profiles. In this article, we conjecture that coherent information structure is a defining feature of complex computation, particularly in biological systems or artificially evolved computation that solves human-understandable tasks. We present a methodology for studying coherent information structure, consisting of state-space diagrams of the local information dynamics and a measure of structure in these diagrams. The methodology identifies both clear and "hidden" coherent structure in complex computation, most notably reconciling conflicting interpretations of the complexity of the Elementary Cellular Automata rule 22.
  Theory in Biosciences 11/2011; 131(3):193-203. · 0.98 Impact Factor
• Source

  Available from: lizier.me

  Article: Relating Fisher information to order parameters.

  Mikhail Prokopenko, Joseph T Lizier, Oliver Obst, X Rosalind Wang
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  ABSTRACT: We study phase transitions and relevant order parameters via statistical estimation theory using the Fisher information matrix. The assumptions that we make limit our analysis to order parameters representable as a negative derivative of thermodynamic potential over some thermodynamic variable. Nevertheless, the resulting representation is sufficiently general and explicitly relates elements of the Fisher information matrix to the rate of change in the corresponding order parameters. The obtained relationships allow us to identify, in particular, second-order phase transitions via divergences of individual elements of the Fisher information matrix. A computational study of random Boolean networks supports the derived relationships, illustrating that Fisher information of the magnetization bias (that is, activity level) is peaked in finite-size networks at the critical points, and the maxima increase with the network size. The framework presented here reveals the basic thermodynamic reasons behind similar empirical observations reported previously. The study highlights the generality of Fisher information as a measure that can be applied to a broad range of systems, particularly those where the determination of order parameters is cumbersome.
  Physical Review E 10/2011; 84(4 Pt 1):041116. · 2.26 Impact Factor
• Source

  Available from: lizier.me

  Article: Information dynamics in small-world Boolean networks.

  Joseph T Lizier, Siddharth Pritam, Mikhail Prokopenko
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  ABSTRACT: Small-world networks have been one of the most influential concepts in complex systems science, partly due to their prevalence in naturally occurring networks. It is often suggested that this prevalence is due to an inherent capability to store and transfer information efficiently. We perform an ensemble investigation of the computational capabilities of small-world networks as compared to ordered and random topologies. To generate dynamic behavior for this experiment, we imbue the nodes in these networks with random Boolean functions. We find that the ordered phase of the dynamics (low activity in dynamics) and topologies with low randomness are dominated by information storage, while the chaotic phase (high activity in dynamics) and topologies with high randomness are dominated by information transfer. Information storage and information transfer are somewhat balanced (crossed over) near the small-world regime, providing quantitative evidence that small-world networks do indeed have a propensity to combine comparably large information storage and transfer capacity.
  Artificial Life 07/2011; 17(4):293-314. · 2.28 Impact Factor