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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.”

References

  • Anderson, D. F., & Higham, D. J. (2012). Multilevel monte carlo for continuous time markov chains, with applications in biochemical kinetics. Multiscale Modeling & Simulation, 10(1), 146–179.

    Article  CAS  Google Scholar 

  • Anderson, D. F., Higham, D. J., & Sun, Y. (2014). Complexity of multilevel monte carlo tau-leaping. SIAM Journal on Numerical Analysis, 52(6), 3106–3127.

    Article  Google Scholar 

  • Anderson, D. F., & Yuan, C. (2019). Low variance couplings for stochastic models of intracellular processes with time-dependent rate functions. Bulletin of mathematical biology, 81(8), 2902–2930.

    Article  CAS  Google Scholar 

  • Chariker, L., & Young, L. S. (2015). Emergent spike patterns in neuronal populations. Journal of computational neuroscience, 38(1), 203–220.

    Article  Google Scholar 

  • Giles, M. B. (2008). Multilevel monte carlo path simulation. Operations research, 56(3), 607–617.

    Article  Google Scholar 

  • Hammersley, J. M., & Handscomb, D. C. (1965). Monte Carlo methods. Methuen & Co., Ltd., London; Barnes & Noble, Inc., New York.

  • Lajoie, G., Lin, K. K., Thivierge, J. P., & Shea-Brown, E. (2016a). Encoding in balanced networks: Revisiting spike patterns and chaos in stimulus-driven systems. PLoS computational biology, 12(12).

  • Lajoie, G., Lin, K. K., Thivierge, J. P., & Shea-Brown, E. (2016b). Revisiting chaos in stimulus-driven spiking networks: signal encoding and discrimination. arXiv preprint https://arxiv.org/abs/1604.07497

  • Lin, K. K. (2013). Stimulus-response reliability of biological networks. In: Nonautonomous Dynamical Systems in the Life Sciences, pp. 135–161. Springer.

  • Lin, K. K., Shea-Brown, E., & Young, L. S. (2009). Reliability of coupled oscillators. Journal of nonlinear science, 19(5), 497–545.

    Article  Google Scholar 

  • Lin, K. K., Shea-Brown, E., & Young, L. S. (2009). Spike-time reliability of layered neural oscillator networks. Journal of computational neuroscience, 27(1), 135–160.

    Article  Google Scholar 

  • London, M., Roth, A., Beeren, L., Häusser, M., & Latham, P. E. (2010). Sensitivity to perturbations in vivo implies high noise and suggests rate coding in cortex. Nature, 466(7302), 123–127.

    Article  CAS  Google Scholar 

  • Rangan, A. V., & Young, L. S. (2013). Dynamics of spiking neurons: between homogeneity and synchrony. Journal of Computational Neuroscience, 34(3), 433–460.

    Article  Google Scholar 

  • Zhang, J., Newhall, K., Zhou, D., & Rangan, A. (2014). Distribution of correlated spiking events in a population-based approach for integrate-and-fire networks. Journal of computational neuroscience, 36(2), 279–295.

    Article  Google Scholar 

Download references

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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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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