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Multilevel monte carlo for cortical circuit models

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Abstract

Multilevel Monte Carlo (MLMC) methods aim to speed up computation of statistics from dynamical simulations. MLMC is easy to implement and is sometimes very effective, but its efficacy may depend on the underlying dynamics. We apply MLMC to networks of spiking neurons and assess its effectiveness on prototypical models of cortical circuitry under different conditions. We find that MLMC can be very efficient for computing reliable features, i.e., features of network dynamics that are reproducible upon repeated presentation of the same external forcing. In contrast, MLMC is less effective for complex, internally generated activity. Qualitative explanations are given using concepts from random dynamical systems theory.

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Data and code availability

Figure data and program source code are available at https://github.com/Texense/UA_MLMC_JCNS.

Notes

  1. Mathematically, one can replace the original state space by path segments of duration \(\Delta\); spike counts are then functions of this augmented “state.”

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Funding

This work has been supported in part by NSF grant DMS-1821286.

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Authors and Affiliations

  1. School of Mathematical Sciences, University of Arizona, Tucson, Arizona, USA

    Kevin K. Lin

  2. Courant Institute of Mathematical Sciences, New York University, New York, USA

    Zhuo-Cheng Xiao

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  1. Zhuo-Cheng Xiao
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  2. Kevin K. Lin
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Correspondence to Zhuo-Cheng Xiao.

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Action Editor: Bard Ermentrout

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Xiao, ZC., Lin, K.K. Multilevel monte carlo for cortical circuit models. J Comput Neurosci 50, 9–15 (2022). https://doi.org/10.1007/s10827-021-00807-3

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  • DOI: https://doi.org/10.1007/s10827-021-00807-3

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