Stochastic Optimal Control of Spike Times in Single Neurons

A. Iolov; S. Ditlevsen; A. Longtin

doi:10.1016/b978-0-12-802452-2.00008-1

Stochastic Optimal Control of Spike Times in Single Neurons

A. Iolov^*, S. Ditlevsen, A. Longtin

^*Corresponding author for this work

Department of Mathematical Sciences

Abstract

We consider the application of optimal control techniques to stochastic models of neural firing. There can be many goals for such control. Here we focus on the targeting of the spiking times of the cell, using a time-varying current applied additively to the current balance equation.We review the theory behind the maximum principle for stochastic optimal control, as well as the challenges posed by its numerical implementation. We then discuss dynamic programming methods for such control, and illustrate its implementation for spike time targeting in the leaky integrate-and-fire model with additive Gaussian white noise. The technique is described in the context where the controller has access to the ongoing voltage. The case where only spike times are available is briefly discussed, along with an outlook into future challenges in designing controls for threshold crossing in drift-diffusion processes.

Original language	English
Title of host publication	Closed Loop Neuroscience
Number of pages	11
Publisher	Elsevier Science Inc.
Publication date	29 Sept 2016
Pages	101-111
ISBN (Print)	9780128024522
ISBN (Electronic)	9780128026410
DOIs	https://doi.org/10.1016/b978-0-12-802452-2.00008-1
Publication status	Published - 29 Sept 2016

Keywords

Morris-Lecar model
Noise
Ornstein-Uhlenbeck process
Single neuron
Spike times
Stochastic optimal control

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10.1016/b978-0-12-802452-2.00008-1

Cite this

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Stochastic Optimal Control of Spike Times in Single Neurons

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Keywords

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