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Equation-free analysis of spike-timing-dependent plasticity

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Abstract

Spike-timing-dependent plasticity is the process by which the strengths of connections between neurons are modified as a result of the precise timing of the action potentials fired by the neurons. We consider a model consisting of one integrate-and-fire neuron receiving excitatory inputs from a large number—here, 1000—of Poisson neurons whose synapses are plastic. When correlations are introduced between the firing times of these input neurons, the distribution of synaptic strengths shows interesting, and apparently low-dimensional, dynamical behaviour. This behaviour is analysed in two different parameter regimes using equation-free techniques, which bypass the explicit derivation of the relevant low-dimensional dynamical system. We demonstrate both coarse projective integration (which speeds up the time integration of a dynamical system) and the use of recently developed data mining techniques to identify the appropriate low-dimensional description of the complex dynamical systems in our model.

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Acknowledgments

The work of CRL was supported by the Marsden Fund Council from Government funding, administered by the Royal Society of New Zealand. The work of IGK was supported by the US National Science Foundation.

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Authors and Affiliations

  1. Institute of Natural and Mathematical Sciences, Massey University, Private Bag 102-904 NSMC, Auckland, New Zealand

    Carlo R. Laing

  2. Department of Chemical and Biological Engineering, Program in Applied and Computational Mathematics, Princeton University, Princeton, NJ, 08544, USA

    Ioannis G. Kevrekidis

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  1. Carlo R. Laing
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Correspondence to Carlo R. Laing.

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Laing, C.R., Kevrekidis, I.G. Equation-free analysis of spike-timing-dependent plasticity. Biol Cybern 109, 701–714 (2015). https://doi.org/10.1007/s00422-015-0668-0

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