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Ergodicity of spike trains: when does trial averaging make sense?

Authors:

Kazuyuki AiharaAuthors Info & Claims

Neural Computation, Volume 15, Issue 6

Pages 1341 - 1372

https://doi.org/10.1162/089976603321780308

Published: 01 June 2003 Publication History

Abstract

Neuronal information processing is often studied on the basis of spiking patterns. The relevant statistics such as firing rates calculated with the peri-stimulus time histogram are obtained by averaging spiking patterns over many experimental runs. However, animals should respond to one experimental stimulation in real situations, and what is available to the brain is not the trial statistics but the population statistics. Consequently, physiological ergodicity, namely, the consistency between trial averaging and population averaging, is implicitly assumed in the data analyses, although it does not trivially hold true. In this letter, we investigate how characteristics of noisy neural network models, such as single neuron properties, external stimuli, and synaptic inputs, affect the statistics of firing patterns. In particular, we show that how high membrane potential sensitivity to input fluctuations, inability of neurons to remember past inputs, external stimuli with large variability and temporally separated peaks, and relatively few contributions of synaptic inputs result in spike trains that are reproducible over many trials. The reproducibility of spike trains and synchronous firing are contrasted and related to the ergodicity issue. Several numerical calculations with neural network examples are carried out to support the theoretical results.

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Cited By

Masuda NDoiron BLongtin AAihara K(2019)Coding of Temporally Varying Signals in Networks of Spiking Neurons with Global Delayed FeedbackNeural Computation10.1162/089976605461568017:10(2139-2175)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1162/0899766054615680
Orcioni SPaffi ACamera FApollonio FLiberti M(2017)Automatic decoding of input sinusoidal signal in a neuron modelNeurocomputing10.1016/j.neucom.2017.06.029267:C(605-614)Online publication date: 6-Dec-2017
https://dl.acm.org/doi/10.1016/j.neucom.2017.06.029

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Ergodicity of spike trains: when does trial averaging make sense?

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cover image Neural Computation

Neural Computation Volume 15, Issue 6

June 2003

246 pages

ISSN:0899-7667

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MIT Press

Cambridge, MA, United States

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Published: 01 June 2003

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Cited By

Masuda NDoiron BLongtin AAihara K(2019)Coding of Temporally Varying Signals in Networks of Spiking Neurons with Global Delayed FeedbackNeural Computation10.1162/089976605461568017:10(2139-2175)Online publication date: 6-Jan-2019
https://dl.acm.org/doi/10.1162/0899766054615680
Orcioni SPaffi ACamera FApollonio FLiberti M(2017)Automatic decoding of input sinusoidal signal in a neuron modelNeurocomputing10.1016/j.neucom.2017.06.029267:C(605-614)Online publication date: 6-Dec-2017
https://dl.acm.org/doi/10.1016/j.neucom.2017.06.029

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