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Neural Computation

Monthly
288 pp. per issue, 6 x 9,
illustrated
Founded: 1989
ISSN 0899-7667
E-ISSN 1530-888X
2007 ISI Impact Factor: 2.335

Neural Computation

January 2007, Vol. 19, No. 1, Pages 47-79
Posted Online November 29, 2006.
(doi:10.1162/neco.2007.19.1.47)
© 2006 Massachusetts Institute of Technology
Exact Subthreshold Integration with Continuous Spike Times in Discrete-Time Neural Network Simulations

Abigail Morrison

Computational Neurophysics, Institute of Biology III, and Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, 79104 Freiburg, Germany,

Sirko Straube

Computational Neurophysics, Institute of Biology III, Albert-Ludwigs-University, 79104 Freiburg, Germany,

Hans Ekkehard Plesser

Department of Mathematical Sciences and Technology, Norwegian University of Life Sciences, N-1432 Ås, Norway,

Markus Diesmann

Computational Neurophysics, Institute of Biology III, and Bernstein Center for Computational Neuroscience, Albert-Ludwigs-University, 79104 Freiburg, Germany,

PDF (245.806 KB) PDF Plus (280.057 KB)

Very large networks of spiking neurons can be simulated efficiently in parallel under the constraint that spike times are bound to an equidistant time grid. Within this scheme, the subthreshold dynamics of a wide class of integrate-and-fire-type neuron models can be integrated exactly from one grid point to the next. However, the loss in accuracy caused by restricting spike times to the grid can have undesirable consequences, which has led to interest in interpolating spike times between the grid points to retrieve an adequate representation of network dynamics. We demonstrate that the exact integration scheme can be combined naturally with off-grid spike events found by interpolation. We show that by exploiting the existence of a minimal synaptic propagation delay, the need for a central event queue is removed, so that the precision of event-driven simulation on the level of single neurons is combined with the efficiency of time-driven global scheduling. Further, for neuron models with linear subthreshold dynamics, even local event queuing can be avoided, resulting in much greater efficiency on the single-neuron level. These ideas are exemplified by two implementations of a widely used neuron model. We present a measure for the efficiency of network simulations in terms of their integration error and show that for a wide range of input spike rates, the novel techniques we present are both more accurate and faster than standard techniques.

Cited by

Ştefan Mihalaş, Ernst Niebur. (2009) A Generalized Linear Integrate-and-Fire Neural Model Produces Diverse Spiking Behaviors. Neural Computation 21:3, 704-718
Online publication date: 1-Mar-2009.
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Hans E. Plesser, Markus Diesmann. (2009) Simplicity and Efficiency of Integrate-and-Fire Neuron Models. Neural Computation 21:2, 353-359
Online publication date: 1-Feb-2009.
Abstract | Full Text | PDF (59 KB) | PDF Plus (60 KB) 
William W. Lytton, Ahmet Omurtag, Samuel A. Neymotin, Michael L. Hines. (2008) Just-in-Time Connectivity for Large Spiking Networks. Neural Computation 20:11, 2745-2756
Online publication date: 1-Nov-2008.
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Michiel D'Haene, Benjamin Schrauwen, Jan Van Campenhout, Dirk Stroobandt. Accelerating Event-Driven Simulation of Spiking Neurons with Multiple Synaptic Time Constants. Neural Computation 0:0, 1-32
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J. H. van Hateren. (2008) Fast Recursive Filters for Simulating Nonlinear Dynamic Systems. Neural Computation 20:7, 1821-1846
Online publication date: 1-Jul-2008.
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Abigail Morrison, Ad Aertsen, Markus Diesmann. (2007) Spike-Timing-Dependent Plasticity in Balanced Random Networks. Neural Computation 19:6, 1437-1467
Online publication date: 1-Jun-2007.
Abstract | PDF (851 KB) | PDF Plus (863 KB) 

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