Conservation laws by virtue of scale symmetries in neural systems
File(s)
Author(s)
Type
Journal Article
Abstract
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, . 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.
Date Issued
2020-05-04
Date Acceptance
2020-04-10
Citation
PLoS Computational Biology, 2020, 16 (5)
ISSN
1553-734X
Publisher
Public Library of Science (PLoS)
Journal / Book Title
PLoS Computational Biology
Volume
16
Issue
5
Copyright Statement
© 2020 Fagerholm et al. This is an open access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
License URL
Identifier
https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1007865
Subjects
Bioinformatics
01 Mathematical Sciences
06 Biological Sciences
08 Information and Computing Sciences
Publication Status
Published
Article Number
e1007865