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Maintaining Causality in Discrete Time Neuronal Network Simulations

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Part of the book series: Understanding Complex Systems ((UCS))

Summary

When designing a discrete time simulation tool for neuronal networks, conceptual difficulties are often encountered in defining the interaction between the continuous dynamics of the neurons and the point events (spikes) they exchange. These problems increase significantly when the tool is designed to be distributed over many computers. In this chapter, we bring together the methods that have been developed over the last years to handle these difficulties. We describe a framework in which the temporal order of events within a simulation remains consistent. It is applicable to networks of neurons with arbitrary subthreshold dynamics, both with and without delays, exchanging point events either constrained to a discrete time grid or in continuous time, and is compatible with distributed computing.

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References

  1. Brette, R. (2006). Exact simulation of integrate-and-fire models with synaptic conductances. Neural Comput. 18(8), 2004–2027.

    Google Scholar 

  2. Lytton, W. W., & Hines, M. L. (2005). Independent variable time-step integration of individual neurons for network simulations. Neural Comput. 17, 903–921.

    Article  Google Scholar 

  3. Morrison, A., Mehring, C., Geisel, T., Aertsen, A., & Diesmann, M. (2005). Advancing the boundaries of high connectivity network simulation with distributed computing. Neural Comput. 17(8), 1776–1801.

    Article  MATH  Google Scholar 

  4. Hansel, D., Mato, G., Meunier, C., & Neltner, L. (1998). On numerical simulations of integrate-and-fire neural networks. Neural Comput. 10(2), 467–483.

    Article  Google Scholar 

  5. Shelley, M. J., & Tao, L. (2001). Efficient and accurate time-stepping schemes for integrate-and-fire neuronal networks. J. Comput. Neurosci. 11(2), 111–119.

    Article  Google Scholar 

  6. Morrison, A., Straube, S., Plesser, H. E., & Diesmann, M. (2006). Exact subthreshold integration with continuous spike times in discrete time neural network simulations. Neural Comput. 19, 47–79.

    Article  MathSciNet  Google Scholar 

  7. Rotter, S., & Diesmann, M. (1999). Exact digital simulation of time-invariant linear systems with applications to neuronal modeling. Biol. Cybern. 81(5/6), 381–402.

    Article  MATH  Google Scholar 

  8. Brown, R. (1988). Calendar queues: a fast O(1) priority queue implementation for the simulation event set problem. Communications of the ACM 31(10), 1220–1227.

    Article  Google Scholar 

  9. Braitenberg, V., & Schüz, A. (1991). Anatomy of the Cortex: Statistics and Geometry. Berlin, Heidelberg, New York: Springer-Verlag.

    Google Scholar 

  10. Hammarlund, P., & Ekeberg, O. (1998). Large neural network simulations on multiple hardware platforms. J. Comput. Neurosci. 5(4), 443–459.

    Article  Google Scholar 

  11. Harris, J., Baurick, J., Frye, J., King, J., Ballew, M., Goodman, P., & Drewes, R. (2003). A novel parallel hardware and software solution for a large-scale biologically realistic cortical simulation. Technical report, University of Nevada.

    Google Scholar 

  12. Bi, G.-q., & Poo, M.-m. (1998). Synaptic modifications in cultured hippocampal neurons: Dependence on spike timing, synaptic strength, and postsynaptic cell type. J. Neurosci. 18, 10464–10472.

    Google Scholar 

  13. Markram, H., Lübke, J., Frotscher, M., & Sakmann, B. (1997). Regulation of synaptic efficacy by coincidence of postsynaptic APs and EPSPs. Science 275, 213–215.

    Article  Google Scholar 

  14. Morrison, A., Aertsen, A., & Diesmann, M. (2007). Spike-timing dependent plasticity in balanced random networks. Neural Comp. 19, 1437–1467.

    Article  MATH  MathSciNet  Google Scholar 

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Morrison, A., Diesmann, M. (2007). Maintaining Causality in Discrete Time Neuronal Network Simulations. In: Graben, P.b., Zhou, C., Thiel, M., Kurths, J. (eds) Lectures in Supercomputational Neurosciences. Understanding Complex Systems. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73159-7_10

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