dorsal/arxiv
View SchemaMean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex
| Authors | A. Lerchner, G. Sterner, J. Hertz, M. Ahmadi |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0403037 |
| URL | https://arxiv.org/abs/q-bio/0403037 |
Abstract
We present a complete mean field theory for a balanced state of a simple model of an orientation hypercolumn. The theory is complemented by a description of a numerical procedure for solving the mean-field equations quantitatively. With our treatment, we can determine self-consistently both the firing rates and the firing correlations, without being restricted to specific neuron models. Here, we solve the analytically derived mean-field equations numerically for integrate-and-fire neurons. Several known key properties of orientation selective cortical neurons emerge naturally from the description: Irregular firing with statistics close to -- but not restricted to -- Poisson statistics; an almost linear gain function (firing frequency as a function of stimulus contrast) of the neurons within the network; and a contrast-invariant tuning width of the neuronal firing. We find that the irregularity in firing depends sensitively on synaptic strengths. If Fano factors are bigger than 1, then they are so for all stimulus orientations that elicit firing. We also find that the tuning of the noise in the input current is the same as the tuning of the external input, while that for the mean input current depends on both the external input and the intracortical connectivity.
{
"annotation_id": "720b88a2-2cf7-4e46-924c-4ad146138a09",
"date_created": "2026-03-02T18:01:31.681000Z",
"date_modified": "2026-03-02T18:01:31.681000Z",
"file_hash": "efc78bc357c11ceb3789f1fe4fd4fc9847afc2b58ca7213d5683de2a5b8bac06",
"private": false,
"record": {
"abstract": "We present a complete mean field theory for a balanced state of a simple\nmodel of an orientation hypercolumn. The theory is complemented by a\ndescription of a numerical procedure for solving the mean-field equations\nquantitatively. With our treatment, we can determine self-consistently both the\nfiring rates and the firing correlations, without being restricted to specific\nneuron models. Here, we solve the analytically derived mean-field equations\nnumerically for integrate-and-fire neurons. Several known key properties of\norientation selective cortical neurons emerge naturally from the description:\nIrregular firing with statistics close to -- but not restricted to -- Poisson\nstatistics; an almost linear gain function (firing frequency as a function of\nstimulus contrast) of the neurons within the network; and a contrast-invariant\ntuning width of the neuronal firing. We find that the irregularity in firing\ndepends sensitively on synaptic strengths. If Fano factors are bigger than 1,\nthen they are so for all stimulus orientations that elicit firing. We also find\nthat the tuning of the noise in the input current is the same as the tuning of\nthe external input, while that for the mean input current depends on both the\nexternal input and the intracortical connectivity.",
"arxiv_id": "q-bio/0403037",
"authors": [
"A. Lerchner",
"G. Sterner",
"J. Hertz",
"M. Ahmadi"
],
"categories": [
"q-bio.NC"
],
"title": "Mean field theory for a balanced hypercolumn model of orientation selectivity in primary visual cortex",
"url": "https://arxiv.org/abs/q-bio/0403037"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "f3adcce6-3f20-429d-8626-f5f3e4b8e794",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}