Averaging Principles for Markovian Models of Plasticity

Pierpoint, Robert; Vignoud, Gaëtan

doi:10.1007/s10955-021-02785-3

Cited by 5 publications

(17 citation statements)

References 20 publications

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“…The process (Z ε (s)) is not bounded and neither is the differential element N β/ε,Xε (ds) since (β(X ε (s)) is also not bounded. The proof of this tightness result motivates a large part of the most technical estimates of Robert and Vignoud [36].…”

Section: Introductionmentioning

confidence: 62%

“…This is done in the paper Robert and Vignoud [36]. If the model was expressed in terms of functionals of the occupation measure of the type…”

Section: Introductionmentioning

confidence: 99%

“…For our general models of Robert and Vignoud [36] the tightness properties are stated on a, a priori, bounded time interval [0, S 0 ) only. More specifically, it is shown that it may happen that the limit in distribution of (W ε (t 0 )) as ε goes to 0 blows-up, i.e.…”

Section: Introductionmentioning

confidence: 99%

“…For this reason, a scaled version of the stochastic model of [37] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [36] is entirely devoted to the tightness properties used to prove these convergence results.These averaging principles are used to study two important STDP models: pair-based rules and calcium-based rules. Our results are compared with the approximations of neuroscience STDP models.…”

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confidence: 99%

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confidence: 99%

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Stochastic Models of Neural Plasticity: A Scaling Approach

Robert,

Vignoud

2021

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In neuroscience, synaptic plasticity refers to the set of mechanisms driving the dynamics of neuronal connections, called synapses and represented by a scalar value, the synaptic weight. A Spike-Timing Dependent Plasticity (STDP) rule is a biologically-based model representing the time evolution of the synaptic weight as a functional of the past spiking activity of adjacent neurons. A general mathematical framework has been introduced in [37].In this paper we develop and investigate a scaling approach of these models based on several biological assumptions. Experiments show that long-term synaptic plasticity evolves on a much slower timescale than the cellular mechanisms driving the activity of neuronal cells, like their spiking activity or the concentration of various chemical components created/suppressed by this spiking activity. For this reason, a scaled version of the stochastic model of [37] is introduced and a limit theorem, an averaging principle, is stated for a large class of plasticity kernels. A companion paper [36] is entirely devoted to the tightness properties used to prove these convergence results.These averaging principles are used to study two important STDP models: pair-based rules and calcium-based rules. Our results are compared with the approximations of neuroscience STDP models. A class of discrete models of STDP rules is also investigated for the analytical tractability of its limiting dynamical system.

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Section: Introductionmentioning

confidence: 62%

“…This is done in the paper Robert and Vignoud [36]. If the model was expressed in terms of functionals of the occupation measure of the type…”

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%