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Thalamic modulation of cortical linearity across arousal states.

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Paper

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The authors' code

MATLAB · 71 lines · 1.9 KB · CC-BY-4.0

  1. function [lmse,msd] = run_LFA(data_ts,n_lag, exp_var_lim)
  2. %RUN_LFA Summary of this function goes here
  3. % Detailed explanation goes here
  4. %
  5. %
  6. % Input:
  7. % data_ts = 3d matrix(double); variable x time x subj/trial/run
  8. %
  9. % n_lag = Number of future timepoints to predict (scalar int)
  10. %
  11. % exp_var_lim = percentage of explained variance to predict (scalar - double)
  12. %
  15. if nargin < 2
  16. n_lag = 10; % Number of future time-points to predict
  17. end
  18. if nargin < 3
  19. exp_var_lim = 99; % Variance explained
  20. end
  23. % Data dimensions
  24. [~,n_time,n_subjs] = size(data_ts);
  27. for subj = 1: n_subjs
  28. subj_ts = data_ts(:,:,subj);
  30. X = subj_ts(:,1:end-1); % X_t
  31. Y = subj_ts(:,2:end); % X_t+1
  33. % SVD
  34. [U, S, V]=svd(X,0); % X = U*S*V'
  36. % ---- Variance Explained
  37. exp_var = 100.*diag(S).^2./sum(diag(S).^2);
  38. accum_exp_var = cumsum(exp_var);
  39. n_pcs = find(accum_exp_var > exp_var_lim,1,'first');
  41. % Reduce rank
  42. U=U(:,1:n_pcs); % Space
  43. V=V(:,1:n_pcs); % Time
  44. S=S(1:n_pcs,1:n_pcs);
  46. % Projection timeseries
  47. X_svd = (S*V.').';
  49. % Estimate linear propagator A_tilde
  50. A_tilde=U'*Y*V/S; % Y = AX -> A = Y*inv(X)
  51. % X = U*S*V'
  54. % ----- Forecast Linear model
  55. % For each timepoint
  56. for ss = 1:n_time-n_lag
  57. X_plus = X_svd(ss,:); % Initialize current point
  58. % For each lag into the future
  59. for ll = 1 : n_lag
  60. % MSE linear model predictions
  61. X_plus(ll+1,:) = A_tilde*X_plus(ll,:).';
  62. lmse(ss,ll,subj) = mean((X_plus(ll,:) - X_svd(ss+ll-1,:)).^2);
  64. % MSD of autocorrelation
  65. msd(ss,ll,subj) = mean((X_svd(ss,:) - X_svd(ss+ll-1,:)).^2);
  66. end
  67. end
  68. %disp(subj)
  69. end
  70. end

run_LFA.m, under CC-BY-4.0 · at the source

Overview

Authors: Eli J. Müller1,2, Brandon R. Munn1,2, Giulia Baracchini1,2, Ben D. Fulcher3, Vicente Medel4,5, Michelle J. Redinbaugh6,7,8, Yuri B. Saalmann7,8, Jordan J. Wehrman9,10, Robert D. Sanders9,10, Bingni W. Brunton11, Steven L. Brunton12, James M. Shine1,2
ORCID iDs: Eli J. Müller, Brandon R. Munn, Giulia Baracchini, Ben D. Fulcher, Vicente Medel, Michelle J. Redinbaugh, Yuri B. Saalmann, Jordan J. Wehrman, Bingni W. Brunton, Steven L. Brunton, James M. Shine
  1. School of Medical Sciences, Faculty of Medicine and Health, The University of Sydney, Sydney, NSW, Australia
  2. Centre for Complex Systems, The University of Sydney, Sydney, NSW, Australia
  3. School of Physics, The University of Sydney, Sydney, NSW, Australia
  4. Latin American Brain Health Institute, Universidad Adolfo Ibañez, Santiago, Chile
  5. Facultad de Ciencias Biológicas, Pontificia Universidad Católica de Chile, Santiago, Chile
  6. Department of Biology, Stanford University, Stanford, CA, USA
  7. Department of Psychology, University of Wisconsin–Madison, Madison, WI, USA
  8. Wisconsin National Primate Research Center, Madison, WI, USA
  9. Central Clinical School, Faculty of Medicine and Health, The University of Sydney, NSW, Australia
  10. Department of Anaesthetics, Royal Prince Alfred Hospital, Sydney Local Health District, NSW, Australia
  11. Department of Biology, University of Washington, Seattle, WA, USA
  12. Department of Mechanical Engineering, University of Washington, Seattle, WA, USA
Institutions: The University of Sydney (Australia); Pontificia Universidad Católica de Chile (Chile); Adolfo Ibáñez University (Chile); University of Wisconsin–Madison (United States); Stanford University (United States); Royal Prince Alfred Hospital (Australia); Sydney Local Health District (Australia); University of Washington (United States)
Journal: Science advances, volume 12, issue 38, article eaef5358
Dates: received 18 January 2026; accepted 7 August 2026; published online 18 September 2026; in print September 2026
Type: Research article · Language: English
License: CC BY-NC
Identifiers: DOI 10.1126/sciadv.aef5358 · PMID 42758834 · PMCID PMC13588182 · OpenAlex W7213562880
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: human (organism)
Methods: Spectral & time-frequency, Connectivity, Smoothing, state filtering, decompositions, Machine learning, Preprocessing, fMRI & imaging, Physiology & signal measures
MeSH: Arousal*, Cerebral Cortex*, Thalamus*, Animals, Brain Mapping, Humans, Magnetic Resonance Imaging, Male (* major topic)
Journal subjects: Neuroscience, Systems Biology
Topic: Functional Brain Connectivity Studies (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: national institutes of health (R01MH110311, P51OD011106, 201732); Alzheimer's Association (25-1490306); Department of Education and Training | Australian Research Council (ARC) (DE250100540, DE260101935); Department of Health | National Health and Medical Research Council (NHMRC) (GNT2033162); ANID Fondecyt de Iniciación (11251578); ANID/FONDECYT Exploración (13240170)
Citations: not cited yet (Europe PMC); 84 references in the paper

Abstract

The human brain must support both stable and flexible neural dynamics to adapt to changing contexts. The thalamus has been hypothesized to coordinate these opposing dynamical regimes in the cerebral cortex; however, this has not been directly tested at the systems level. Here, we apply a time-resolved measure of linearity to multimodal recordings in humans and macaques, demonstrating irregular fluctuations in both human functional magnetic resonance imaging and electrophysiological in the awake state. These fluctuations follow a key neuroanatomical axis of the thalamus, are diminished under pharmacological ablation of arousal, and recovered following arousal-inducing direct electrical stimulation of thalamus. Together, these findings identify a thalamic organizational axis that modulates cortical linearity across arousal states, linking thalamocortical architecture to the regulation of large-scale cortical dynamics.

Reproduced under the paper's license (CC BY-NC), from the paper cited above.

Repository

Its files are read in the Code ↔ Paper reader above.

Zenodo 19905547

License: CC-BY-4.0
State: the link answers, verified on 26 September 2026
Evidence: files inventoried
Languages: MATLAB (2)
Size: 2 files, 2 scripts
Software Heritage: not checked
Found in: the text, “Linear forecast analysis”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 26 September 2026: the link answers (HTTP 200)
  • 26 September 2026: the link answers (HTTP 200)
2 files
At the source: doi.org/10.5281/zenodo.19905547

The paper's code and data availability statement is in the Data section.

Tracing map

Proposed by the machine: these links were found in the paper and verified at the source, without human review. The map will receive a Zenodo DOI once one of the paper's authors has validated it with their ORCID.

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  • 1 repository of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 2 scripts, each with its path and the digest of its content;
  • no match between paragraphs and code yet;
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Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

Data, code, and materials availability

All data and code needed to evaluate and reproduce the results in the paper are present in the paper and/or the Supplementary Materials. This study did not generate new materials. The human EEG data can be provided by R. A. Pearce (University of Wisconsin) pending scientific review and a completed material transfer agreement through University of Wisconsin. Requests for the EEG data should be submitted to .

Reproduced under the paper's license (CC BY-NC), from the paper cited above.

Versions

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Version 1, 27 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 12 authors, 8 MeSH terms, 6 funders, 75 references.

Cite

This paper

Müller, E. J., Munn, B. R., Baracchini, G., Fulcher, B. D., Medel, V., Redinbaugh, M. J., Saalmann, Y. B., Wehrman, J. J., Sanders, R. D., Brunton, B. W., Brunton, S. L., & Shine, J. M. (2026). Thalamic modulation of cortical linearity across arousal states. Science advances, 12(38), eaef5358. https://doi.org/10.1126/sciadv.aef5358

BibTeX

@article{muller2026thalamic,
author = {Müller, Eli J. and Munn, Brandon R. and Baracchini, Giulia and Fulcher, Ben D. and Medel, Vicente and Redinbaugh, Michelle J. and Saalmann, Yuri B. and Wehrman, Jordan J. and Sanders, Robert D. and Brunton, Bingni W. and Brunton, Steven L. and Shine, James M.},
title = {{Thalamic modulation of cortical linearity across arousal states}},
journal = {Science advances},
year = {2026},
month = sep,
volume = {12},
number = {38},
pages = {eaef5358},
publisher = {American Association for the Advancement of Science},
issn = {2375-2548},
doi = {10.1126/sciadv.aef5358},
url = {https://doi.org/10.1126/sciadv.aef5358},
pmid = {42758834},
pmcid = {PMC13588182}
}

RIS

TY - JOUR
AU - Müller, Eli J.
AU - Munn, Brandon R.
AU - Baracchini, Giulia
AU - Fulcher, Ben D.
AU - Medel, Vicente
AU - Redinbaugh, Michelle J.
AU - Saalmann, Yuri B.
AU - Wehrman, Jordan J.
AU - Sanders, Robert D.
AU - Brunton, Bingni W.
AU - Brunton, Steven L.
AU - Shine, James M.
TI - Thalamic modulation of cortical linearity across arousal states
T2 - Science advances
J2 - Sci Adv
PY - 2026
DA - 2026/09/18
VL - 12
IS - 38
SP - eaef5358
SN - 2375-2548
PB - American Association for the Advancement of Science
DO - 10.1126/sciadv.aef5358
UR - https://doi.org/10.1126/sciadv.aef5358
LA - en
ER -

CSL-JSON

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"family": "Müller",
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"given": "Vicente"
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{
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"given": "Yuri B."
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"container-title-short": "Sci Adv",
"volume": "12",
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"page": "eaef5358",
"DOI": "10.1126/sciadv.aef5358",
"PMID": "42758834",
"PMCID": "PMC13588182",
"ISSN": "2375-2548",
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