The University of Southampton
University of Southampton Institutional Repository

Stability against fluctuations: Scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity

Stability against fluctuations: Scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity
Stability against fluctuations: Scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity
In stochastic models of synaptic plasticity based on a random walk, the control of fluctuations is imperative. We have argued that synapses could act as low-pass filters, filtering plasticity induction steps before expressing a step change in synaptic strength. Earlier work showed, in simulation, that such a synaptic filter tames fluctuations very well, leading to patterns of synaptic connectivity that are stable for long periods of time. Here, we approach this problem analytically. We explicitly calculate the lifetime of meta-stable states of synaptic connectivity using a Fokker-Planck formalism in order to understand the dependence of this lifetime on both the plasticity step size and the filtering mechanism. We find that our analytical results agree very well with simulation results, despite having to make two approximations. Our analysis reveals, however, a deeper significance to the filtering mechanism and the plasticity step size. We show that a filter scales the step size into a smaller, effective step size. This scaling suggests that the step size may itself play the role of a temperature parameter, so that a filter cools the dynamics, thereby reducing the influence of fluctuations. Using the master equation, we explicitly demonstrate a bifurcation at a critical step size, confirming this interpretation. At this critical point, spontaneous symmetry breaking occurs in the class of stochastic models of synaptic plasticity that we consider.
674-734
Elliott, Terry
b4262f0d-c295-4ea4-b5d8-3931470952f9
Elliott, Terry
b4262f0d-c295-4ea4-b5d8-3931470952f9

Elliott, Terry (2011) Stability against fluctuations: Scaling, bifurcations and spontaneous symmetry breaking in stochastic models of synaptic plasticity. Neural Computation, 23 (3), 674-734. (doi:10.1162/NECO_a_00088). (PMID:21162665)

Record type: Article

Abstract

In stochastic models of synaptic plasticity based on a random walk, the control of fluctuations is imperative. We have argued that synapses could act as low-pass filters, filtering plasticity induction steps before expressing a step change in synaptic strength. Earlier work showed, in simulation, that such a synaptic filter tames fluctuations very well, leading to patterns of synaptic connectivity that are stable for long periods of time. Here, we approach this problem analytically. We explicitly calculate the lifetime of meta-stable states of synaptic connectivity using a Fokker-Planck formalism in order to understand the dependence of this lifetime on both the plasticity step size and the filtering mechanism. We find that our analytical results agree very well with simulation results, despite having to make two approximations. Our analysis reveals, however, a deeper significance to the filtering mechanism and the plasticity step size. We show that a filter scales the step size into a smaller, effective step size. This scaling suggests that the step size may itself play the role of a temperature parameter, so that a filter cools the dynamics, thereby reducing the influence of fluctuations. Using the master equation, we explicitly demonstrate a bifurcation at a critical step size, confirming this interpretation. At this critical point, spontaneous symmetry breaking occurs in the class of stochastic models of synaptic plasticity that we consider.

Full text not available from this repository.

More information

e-pub ahead of print date: 1 February 2011
Published date: March 2011
Organisations: Web & Internet Science

Identifiers

Local EPrints ID: 272302
URI: http://eprints.soton.ac.uk/id/eprint/272302
PURE UUID: 4268debb-6b68-411d-9e92-e4747eb7e25b

Catalogue record

Date deposited: 18 May 2011 12:46
Last modified: 16 Jul 2019 22:14

Export record

Altmetrics

Download statistics

Downloads from ePrints over the past year. Other digital versions may also be available to download e.g. from the publisher's website.

View more statistics

Atom RSS 1.0 RSS 2.0

Contact ePrints Soton: eprints@soton.ac.uk

ePrints Soton supports OAI 2.0 with a base URL of http://eprints.soton.ac.uk/cgi/oai2

This repository has been built using EPrints software, developed at the University of Southampton, but available to everyone to use.

We use cookies to ensure that we give you the best experience on our website. If you continue without changing your settings, we will assume that you are happy to receive cookies on the University of Southampton website.

×