| Title |
Finite-Size Effects on Traveling Wave Solutions to Neural Field Equations
|
|---|---|
| Published in |
The Journal of Mathematical Neuroscience, July 2017
|
| DOI | 10.1186/s13408-017-0048-2 |
| Pubmed ID | |
| Authors |
Eva Lang, Wilhelm Stannat |
| Abstract |
Neural field equations are used to describe the spatio-temporal evolution of the activity in a network of synaptically coupled populations of neurons in the continuum limit. Their heuristic derivation involves two approximation steps. Under the assumption that each population in the network is large, the activity is described in terms of a population average. The discrete network is then approximated by a continuum. In this article we make the two approximation steps explicit. Extending a model by Bressloff and Newby, we describe the evolution of the activity in a discrete network of finite populations by a Markov chain. In order to determine finite-size effects-deviations from the mean-field limit due to the finite size of the populations in the network-we analyze the fluctuations of this Markov chain and set up an approximating system of diffusion processes. We show that a well-posed stochastic neural field equation with a noise term accounting for finite-size effects on traveling wave solutions is obtained as the strong continuum limit. |
X Demographics
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Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 3 | 100% |
Demographic breakdown
| Type | Count | As % |
|---|---|---|
| Members of the public | 2 | 67% |
| Scientists | 1 | 33% |
Mendeley readers
The data shown below were compiled from readership statistics for 9 Mendeley readers of this research output. Click here to see the associated Mendeley record.
Geographical breakdown
| Country | Count | As % |
|---|---|---|
| Unknown | 9 | 100% |
Demographic breakdown
| Readers by professional status | Count | As % |
|---|---|---|
| Researcher | 5 | 56% |
| Professor | 1 | 11% |
| Student > Ph. D. Student | 1 | 11% |
| Student > Postgraduate | 1 | 11% |
| Unknown | 1 | 11% |
| Readers by discipline | Count | As % |
|---|---|---|
| Mathematics | 3 | 33% |
| Physics and Astronomy | 1 | 11% |
| Social Sciences | 1 | 11% |
| Medicine and Dentistry | 1 | 11% |
| Unknown | 3 | 33% |
Attention Score in Context
This research output has an Altmetric Attention Score of 2. This is our high-level measure of the quality and quantity of online attention that it has received. This Attention Score, as well as the ranking and number of research outputs shown below, was calculated when the research output was last mentioned on 08 July 2017.
All research outputs
#15,749,194
of 25,385,509 outputs
Outputs from The Journal of Mathematical Neuroscience
#31
of 79 outputs
Outputs of similar age
#179,609
of 326,054 outputs
Outputs of similar age from The Journal of Mathematical Neuroscience
#2
of 3 outputs
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So far Altmetric has tracked 79 research outputs from this source. They receive a mean Attention Score of 2.7. This one has gotten more attention than average, scoring higher than 58% of its peers.
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