dorsal/arxiv
View SchemaAdaptation and regulation with signal detection implies internal model
| Authors | Eduardo D. Sontag |
|---|---|
| Categories | |
| ArXiv ID | q-bio/0309003 |
| URL | https://arxiv.org/abs/q-bio/0309003 |
Abstract
This note provides a theorem showing, under suitable technical assumptions, that if a system S adapts to a class of external signals U, in the sense of egulation against disturbances or tracking signals in U, then S must ecessarily contain a subsystem which is capable of generating all the signals in U. It is not assumed that regulation is robust, nor is there a prior requirement for the system to be partitioned into separate plant and controller components. Instead, one assumes that a ``signal detection'' property holds. The result was motivated by questions of adaptation in bacterial chemotaxis, but the general mathematical principle is of wide applicability.
{
"annotation_id": "85227085-3fd6-4884-84f0-e2e18bf9f90b",
"date_created": "2026-03-02T18:01:28.643000Z",
"date_modified": "2026-03-02T18:01:28.643000Z",
"file_hash": "56b14c3e3914fb46ad00b40bb4ebd48feaa9c62ae14bf270962f7a7aac721c9f",
"private": false,
"record": {
"abstract": "This note provides a theorem showing, under suitable technical assumptions,\nthat if a system S adapts to a class of external signals U, in the sense of\negulation against disturbances or tracking signals in U, then S must ecessarily\ncontain a subsystem which is capable of generating all the signals in U. It is\nnot assumed that regulation is robust, nor is there a prior requirement for the\nsystem to be partitioned into separate plant and controller components.\nInstead, one assumes that a ``signal detection\u0027\u0027 property holds. The result was\nmotivated by questions of adaptation in bacterial chemotaxis, but the general\nmathematical principle is of wide applicability.",
"arxiv_id": "q-bio/0309003",
"authors": [
"Eduardo D. Sontag"
],
"categories": [
"q-bio.QM",
"q-bio.MN"
],
"title": "Adaptation and regulation with signal detection implies internal model",
"url": "https://arxiv.org/abs/q-bio/0309003"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "c31c63bc-eaad-423f-ab2d-472a59cfd60b",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}