Conservation laws by virtue of scale symmetries in neural systems.
Journal
PLoS computational biology
ISSN: 1553-7358
Titre abrégé: PLoS Comput Biol
Pays: United States
ID NLM: 101238922
Informations de publication
Date de publication:
05 2020
05 2020
Historique:
received:
26
11
2019
accepted:
10
04
2020
revised:
14
05
2020
pubmed:
5
5
2020
medline:
29
8
2020
entrez:
5
5
2020
Statut:
epublish
Résumé
In contrast to the symmetries of translation in space, rotation in space, and translation in time, the known laws of physics are not universally invariant under transformation of scale. However, a special case exists in which the action is scale invariant if it satisfies the following two constraints: 1) it must depend upon a scale-free Lagrangian, and 2) the Lagrangian must change under scale in the same way as the inverse time, [Formula: see text]. Our contribution lies in the derivation of a generalised Lagrangian, in the form of a power series expansion, that satisfies these constraints. This generalised Lagrangian furnishes a normal form for dynamic causal models-state space models based upon differential equations-that can be used to distinguish scale symmetry from scale freeness in empirical data. We establish face validity with an analysis of simulated data, in which we show how scale symmetry can be identified and how the associated conserved quantities can be estimated in neuronal time series.
Identifiants
pubmed: 32365069
doi: 10.1371/journal.pcbi.1007865
pii: PCOMPBIOL-D-19-02042
pmc: PMC7224579
doi:
Types de publication
Journal Article
Research Support, Non-U.S. Gov't
Langues
eng
Sous-ensembles de citation
IM
Pagination
e1007865Subventions
Organisme : Medical Research Council
ID : MR/R005370/1
Pays : United Kingdom
Organisme : Wellcome Trust
ID : 088130/Z/09/Z
Pays : United Kingdom
Organisme : Wellcome Trust
ID : 203148/Z/16/Z
Pays : United Kingdom
Organisme : Department of Health
Pays : United Kingdom
Déclaration de conflit d'intérêts
The authors have declared that no competing interests exist.
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