Currently Reading

Xiaojuan Sun, Matjaz Perc, Qishao Lu, and Jürgen Kurths, “Spatial coherence resonance on diffusive and small-world networks of Hodgkin-Huxley neurons” (arXiv:0803.0070, accepted for publication in Chaos).

Spatial coherence resonance in a spatially extended system that is locally modeled by Hodgkin-Huxley (HH) neurons is studied in this paper. We focus on the ability of additive temporally and spatially uncorrelated Gaussian noise to extract a particular spatial frequency of excitatory waves in the medium, whereby examining also the impact of diffusive and small-world network topology determining the interactions amongst coupled HH neurons. We show that there exists an intermediate noise intensity that is able to extract a characteristic spatial frequency of the system in a resonant manner provided the latter is diffusively coupled, thus indicating the existence of spatial coherence resonance. However, as the diffusive topology of the medium is relaxed via the introduction of shortcut links introducing small-world properties amongst coupled HH neurons, the ability of additive Gaussian noise to evoke ordered excitatory waves deteriorates rather spectacularly, leading to the decoherence of the spatial dynamics and with it related absence of spatial coherence resonance. In particular, already a minute fraction of shortcut links suffices to substantially disrupt coherent pattern formation in the examined system.

The sensitivity of a spatially distributed network model to added “shortcut links” is an interesting general question.

One thought on “Currently Reading”

  1. Neat. One of my fave. papers by Jon Kleinberg explores something similar (http://www.cs.cornell.edu/home/kleinber/nat00.pdf). A number of nodes are spatially distributed and connected to all its neighbors. Then each node is connected randomly to some other remote node with a probability inversely proportional to distance. The global average communication time is minimized when the coefficient on that probability is 2 – that is, inverse squared.

    In terms of brains, I guess that even though shortcut links disrupt some groups, it improves the overall communication of all the neurons… to a point… too many links and you lose coherency… or something… sociologist, I don’t know brains that well. I think it’s a really amazing question.

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