dorsal/arxiv
View SchemaVariable-free exploration of stochastic models: a gene regulatory network example
| Authors | Radek Erban, Thomas A. Frewen, Xiao Wang, Timothy C. Elston, Ronald Coifman, Boaz Nadler, Ioannis G. Kevrekidis |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0611022 |
| URL | https://arxiv.org/abs/q-bio/0611022 |
| DOI | 10.1063/1.2718529 |
Abstract
Finding coarse-grained, low-dimensional descriptions is an important task in the analysis of complex, stochastic models of gene regulatory networks. This task involves (a) identifying observables that best describe the state of these complex systems and (b) characterizing the dynamics of the observables. In a previous paper [13], we assumed that good observables were known a priori, and presented an equation-free approach to approximate coarse-grained quantities (i.e, effective drift and diffusion coefficients) that characterize the long-time behavior of the observables. Here we use diffusion maps [9] to extract appropriate observables ("reduction coordinates") in an automated fashion; these involve the leading eigenvectors of a weighted Laplacian on a graph constructed from network simulation data. We present lifting and restriction procedures for translating between physical variables and these data-based observables. These procedures allow us to perform equation-free coarse-grained, computations characterizing the long-term dynamics through the design and processing of short bursts of stochastic simulation initialized at appropriate values of the data-based observables.
{
"annotation_id": "7f9d0ed2-1a47-4694-801c-d385f1137343",
"date_created": "2026-03-02T18:01:35.542000Z",
"date_modified": "2026-03-02T18:01:35.542000Z",
"file_hash": "1f57eb3e031b3a4c14c94d5c1acb8214c801cc88c5ef416fea7a56f666469490",
"private": false,
"record": {
"abstract": "Finding coarse-grained, low-dimensional descriptions is an important task in\nthe analysis of complex, stochastic models of gene regulatory networks. This\ntask involves (a) identifying observables that best describe the state of these\ncomplex systems and (b) characterizing the dynamics of the observables. In a\nprevious paper [13], we assumed that good observables were known a priori, and\npresented an equation-free approach to approximate coarse-grained quantities\n(i.e, effective drift and diffusion coefficients) that characterize the\nlong-time behavior of the observables. Here we use diffusion maps [9] to\nextract appropriate observables (\"reduction coordinates\") in an automated\nfashion; these involve the leading eigenvectors of a weighted Laplacian on a\ngraph constructed from network simulation data. We present lifting and\nrestriction procedures for translating between physical variables and these\ndata-based observables. These procedures allow us to perform equation-free\ncoarse-grained, computations characterizing the long-term dynamics through the\ndesign and processing of short bursts of stochastic simulation initialized at\nappropriate values of the data-based observables.",
"arxiv_id": "q-bio/0611022",
"authors": [
"Radek Erban",
"Thomas A. Frewen",
"Xiao Wang",
"Timothy C. Elston",
"Ronald Coifman",
"Boaz Nadler",
"Ioannis G. Kevrekidis"
],
"categories": [
"q-bio.QM",
"physics.comp-ph",
"q-bio.MN"
],
"doi": "10.1063/1.2718529",
"title": "Variable-free exploration of stochastic models: a gene regulatory network example",
"url": "https://arxiv.org/abs/q-bio/0611022"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b2871e1b-c903-4970-9f9e-396eeb80bd92",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}