Lai, YM and De Kamps, M orcid.org/0000-0001-7162-4425 (2017) Population Density Equations for Stochastic Processes with Memory Kernels. Physical Review E, 95 (6). 062125. ISSN 1539-3755
Abstract
We present a novel method for solving population density equations (PDEs) - a mean field technique describing homogeneous populations of uncoupled neurons - where the populations can be subject to non-Markov noise for arbitrary distributions of jump sizes. The method combines recent developments in two different disciplines that traditionally have had limited interaction: computational neuroscience and the theory of random networks. The method uses a geometric binning scheme, based on the method of characteristics, to capture the deterministic neurodynamics of the population, separating the deterministic and stochastic process cleanly. We can independently vary the choice of the deterministic model and the model for the stochastic process, leading to a highly modular numerical solution strategy. We demonstrate this by replacing the Master equation implicit in many formulations of the PDE formalism, by a generalization called the generalized Montroll-Weiss equation - a recent result from random network theory - describing a random walker subject to transitions realized by a non-Markovian process. We demonstrate the method for leaky- (LIF) and quadratic-integrate and fire (QIF) neurons subject to spike trains with Poisson and gamma distributed interspike intervals. We are able to model jump responses for both models accurately to both excitatory and inhibitory input under the assumption that all inputs are generated by one renewal process.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © 2017 American Physical Society. This is the published version of a paper published in Physical Review E. Uploaded in accordance with the publisher's self-archiving policy. |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) |
Funding Information: | Funder Grant number EU - European Union GA 720270 |
Depositing User: | Symplectic Publications |
Date Deposited: | 18 May 2017 10:05 |
Last Modified: | 13 May 2019 09:56 |
Published Version: | https://journals.aps.org/pre/accepted/f5072Rb7A951... |
Status: | Published |
Publisher: | American Physical Society |
Identification Number: | 10.1103/PhysRevE.95.062125 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:116609 |