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Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue.

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MATLAB · 534 lines · 15 KB · no license

  2. %% Function to fit different perceived effort models to the effort rating data (Experiment 1) in Müller, Milton, Husain, & Apps (2026, CABN)
  3. % Available on OSF: https://doi.org/10.17605/OSF.IO/SB9JF
  5. % The code is based on the fatigue modelling implemented in
  6. % T. Müller, M.C. Klein-Flügge, S.G. Manohar, M. Husain, & M.A.J. Apps (2021, Nature Communications)
  7. % and in J. Matthews, M. A. Pisauro, M. Jurgelis, T. Müller, E. Vassena, T. T.-J. Chong, & M.A.J. Apps (2023, Cognition)
  8. % - both manuscripts published under this license:
  9. % https://creativecommons.org/licenses/by/4.0/ -
  10. % and has been modified accordingly by T.M. for this manuscript.
  13. % Please note:
  15. % Participant data are stored in/taken from "s".
  17. % Although some variable names include the term "choice", in these tasks participants were not actually required to make any choices
  18. % (see associated manuscript text for details).
  20. % The order (numbers) of the models in this script differ(s) from the order (numbers) in the manuscript.
  21. % ST refers to recoverable fatigue, LT refers to unrecoveralbe fatigue as described in the manuscript.
  23. % The script uses a separate function "allcomb", available for example on MATLAB Central File Exchange
  24. % (https://www.mathworks.com/matlabcentral/fileexchange/10064-allcomb-varargin), Copyright (c) 2018, Jos (10584).
  27. %%
  29. function sf_model_results = ModellingCode_Experiment1_MullerEtAl2026CABN(s)
  31. close all
  33. N = max(size(s));
  34. %% Fatigue Models
  35. test_models = [1, 2, 3, 4, 5, 6]; % which models you wish to test(e.g. 1 = fat_v1, 2 = fat_just_LT, ...)
  36. model_names = {'fat_v1', 'fat_just_LT', 'fat_one_noLT', 'fat_onepar_withLT', 'fat_noLT', 'noFat_onePara'};
  37. model_names = model_names([test_models]);
  38. fatigue_models = {
  39. @(p,E,fatigue_rating,effort) fat_v1(p,E,fatigue_rating,effort);
  40. @(p,E,fatigue_rating,effort) fat_just_LT(p,E,fatigue_rating,effort);
  41. @(p,E,fatigue_rating,effort) fat_one_noLT(p,E,fatigue_rating,effort);
  42. @(p,E,fatigue_rating,effort) fat_onepar_withLT(p,E,fatigue_rating,effort);
  43. @(p,E,fatigue_rating,effort) fat_noLT(p,E,fatigue_rating,effort);
  44. @(p,E,fatigue_rating,effort) noFat_onePara(p,E,fatigue_rating,effort);
  45. };
  46. model_params = [4, 2, 2, 3, 3, 1]; % Number of parameters in each model
  48. %% Creating empty variables
  49. parameter_estimates_best = [];
  50. Chi_best = []; % We call it Chi here
  51. total_fat_estimate_best = {};
  52. SF_estimate_best = {};
  53. LF_estimate_best = {};
  54. eff_estimate_best = {};
  56. aic = nans(N, max(test_models));
  57. corr = nans(N, max(test_models));
  58. R_sq = nans(N, max(test_models));
  59. R_sq_sig = nans(N, max(test_models));
  60. Chi_best = []; % temp
  62. %% Select Participant
  63. for i=1:N % loops through all subjects
  64. i
  65. %% Select Model
  66. for j = 1:length(test_models)
  67. z = test_models(j);
  68. %% Assign infinity to the initial lss value
  69. Chi_best(i, z) = inf;
  70. %% Load data
  71. E = s(i).choice_fat_squeeze_areaundercurve_norm.*10;
  72. fatigue_rating = s(i).choice_fat_postFatigue; % Note: This is acutally the effort rating in this task!
  74. % Load effort levels to determine rest trials
  75. effort = s(i).choice_fat_effort;
  77. %% Select Fatigue Function and Define Fit Measures Negative Likelihood
  78. fat_func = fatigue_models{z};
  79. Chi = @(p) fat_func(p, E, fatigue_rating, effort);
  81. %% Find the best parameter estimates through repeated ss function minimization
  82. clear startVals
  83. clear constrained_nll
  85. gridVals = [0:0.2:1.0];
  87. % Define constrained ss function
  88. if model_params(z) == 1
  89. startVals = gridVals;
  90. startVals = startVals';
  91. constrained_Chi = @(p) Chi(p) + (p(1)<0)*realmax;
  92. elseif model_params(z) == 2
  93. startVals = allcomb(gridVals,gridVals);
  94. constrained_Chi = @(p) Chi(p) + (p(1)<0)*realmax + (p(2)<0)*realmax;
  95. elseif model_params(z) == 3
  96. startVals = allcomb(gridVals,gridVals,gridVals);
  97. constrained_Chi = @(p) Chi(p) + (p(1)<0)*realmax + (p(2)<0)*realmax + (p(3)<0)*realmax;
  98. elseif model_params(z) == 4
  99. startVals = allcomb(gridVals,gridVals,gridVals,gridVals);
  100. constrained_Chi = @(p) Chi(p) + (p(1)<0)*realmax + (p(2)<0)*realmax + (p(3)<0)*realmax + (p(4)<0)*realmax;
  101. end
  103. % Minimize constrained Chi
  104. ChiBestIter = inf;
  105. for startPIter = 1:size(startVals,1)
  106. startp = startVals(startPIter,:);
  108. [pk, Chik] = fminsearch(constrained_Chi, startp, optimset('MaxFunEvals',10000,'MaxIter',10000));
  110. if Chik<ChiBestIter
  111. ChiBestIter = Chik;
  112. pkBestIter = pk;
  113. end
  114. end
  116. if ChiBestIter < Chi_best(i, z)
  117. parameter_estimates_best{i, z} = pkBestIter;
  118. Chi_best(i, z) = ChiBestIter;
  119. end
  121. sf_model_results.all_Chi(i,z) = ChiBestIter;
  122. sf_model_results.all_p{i,z} = pkBestIter;
  124. aic(i, z) = length(effort)*log(Chi_best(i,z)/length(effort)) + 2*(model_params(z));
  126. [Chi_best(i, z), total_fat_estimate_best{i, z}, st_fat_estimate_best{i, z}, lt_fat_estimate_best{i, z}, eff_estimate_best{i, z}] = fat_func(parameter_estimates_best{i, z}, E, fatigue_rating, effort);
  128. % Non-linear R squared (via correlation)
  129. [R , P] = corrcoef(eff_estimate_best{i, z},fatigue_rating);
  130. corr(i, z) = R(1, 2);
  131. R_sq(i, z) = R(1, 2) ^ 2;
  132. R_sq_sig(i, z) = P(1, 2);
  133. end
  135. end
  138. %% Add results to a structure
  139. sf_model_results.tot_sf_est = total_fat_estimate_best; % best SF (fatigue) estimate for each model, total fatigue
  140. sf_model_results.st_sf_est = st_fat_estimate_best; % best SF estimate for each model, recoverable (short-term) fatigue
  141. sf_model_results.lt_sf_est = lt_fat_estimate_best; % best SF estimate for each model, unrecoverable (long-term) fatigue
  142. sf_model_results.eff_est = eff_estimate_best; % best subjective effort estimate for each model
  143. sf_model_results.corr = corr;
  144. sf_model_results.R_sq = R_sq; % R squared between estimated and reported subjective effort
  145. sf_model_results.R_sq_sig = R_sq_sig; % p value of R squared between estimated and reported subjective effort
  146. sf_model_results.aic = aic;
  147. sf_model_results.Chi = Chi_best;
  148. % Model compared
  149. sf_model_results.models = fatigue_models;
  150. sf_model_results.model_names = model_names;
  151. sf_model_results.model_params = model_params;
  154. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  155. %%%%%%%%%%%%%SUBJECTIVE FATIGUE MODELS%%%%%%%%%%%%
  156. %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
  158. %% Total fatigue estimate 1 (different coefficients for LTfat, STfat Work and Rest)
  159. function [Chi,Fat,STfat,LTfat,Eff] = fat_v1(p, E, fatigue_rating, effort)
  161. %% Regression coefficients
  162. alfa = p(1); % Rest
  163. beta = p(2); % Short-term fatigue (recoverable)
  164. gamma = p(3); % Long-term fatigue (unrecoverable)
  165. delta = p(4); % effort weight
  167. %% Empy arrays for scores
  168. STfat = nans(length(effort), 1);
  169. LTfat = nans(length(effort), 1);
  170. Fat = nans(length(effort), 1);
  171. Eff = nans(length(effort), 1);
  173. %% Starting fatigue values
  174. Fat_startp = 0.01;
  175. ST_fatigue_startp = 0;
  176. LT_fatigue_startp = 0;
  177. %%
  178. for t=1
  179. if effort(t) == 1
  180. STfat(t) = ST_fatigue_startp - (alfa*7.5);
  181. LTfat(t) = LT_fatigue_startp;
  182. else
  183. STfat(t) = ST_fatigue_startp + (beta*E(t)) - (alfa*2.5);
  184. LTfat(t) = LT_fatigue_startp + (gamma*E(t));
  185. end
  186. % Set limits to ST fatigue estimate
  187. if STfat(t) < 0
  188. STfat(t) = 0;
  189. end
  190. % Estimate total fatigue at time point t
  191. Fat(t) = Fat_startp + STfat(t) + LTfat(t);
  193. % Estimate effort at time point t
  194. if effort(t) == 1
  195. Eff(t) = 0;
  196. else
  197. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  198. end
  200. end
  202. for t=2:length(effort)
  203. if effort(t) == 1
  204. STfat(t) = STfat(t-1) - (alfa*7.5);
  205. LTfat(t) = LTfat(t-1);
  206. else
  207. STfat(t) = STfat(t-1) + (beta*E(t)) - (alfa*2.5);
  208. LTfat(t) = LTfat(t-1) + (gamma*E(t));
  209. end
  211. % Set limits to ST fatigue estimate
  212. if STfat(t) < 0
  213. STfat(t) = 0;
  214. end
  215. % Estimate total fatigue at time point t
  216. Fat(t) = Fat_startp + STfat(t) + LTfat(t);
  218. % Estimate effort at time point t
  219. if effort(t) == 1
  220. Eff(t) = 0;
  221. else
  222. Eff(t) =(E(t).*Fat(t)) + (E(t)*delta);
  223. end
  225. end
  226. %% Measures of model fit
  227. residual_squares = ((fatigue_rating - Eff).^2);
  228. Chi = sum(residual_squares); % Chi squared
  230. end
  233. %% Total fatigue estimate 2 (only LTfat)
  234. function [Chi, Fat, STfat, LTfat, Eff] = fat_just_LT(p, E, fatigue_rating, effort)
  236. %% Regression coefficients
  237. gamma = p(1);
  238. delta = p(2);
  240. %% Empy arrays for scores
  241. STfat = nans(length(effort), 1);
  242. LTfat = nans(length(effort), 1);
  243. Fat = nans(length(effort), 1);
  244. Eff = nans(length(effort), 1);
  246. %% Starting fatigue values
  247. Fat_startp = 0.01;
  248. LT_fatigue_startp = 0;
  250. %%
  251. for t=1
  252. if effort(t) == 1
  253. LTfat(t) = LT_fatigue_startp;
  254. else
  255. LTfat(t) = LT_fatigue_startp + (gamma*E(t));
  256. end
  257. % Estimate total fatigue at time point t
  258. Fat(t) = Fat_startp + LTfat(t);
  260. % Estimate effort at time point t
  261. if effort(t) == 1
  262. Eff(t) = 0;
  263. else
  264. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  265. end
  267. end
  269. for t=2:length(effort)
  270. if effort(t) == 1
  271. LTfat(t) = LTfat(t-1);
  272. else
  273. LTfat(t) = LTfat(t-1) + (gamma*E(t));
  274. end
  275. % Estimate total fatigue at time point t
  276. Fat(t) = Fat_startp + LTfat(t);
  278. % Estimate effort at time point t
  279. if effort(t) == 1
  280. Eff(t) = 0;
  281. else
  282. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  283. end
  284. end
  285. %% Fit measures
  286. residual_squares = ((fatigue_rating - Eff).^2);
  287. Chi = sum(residual_squares); % Chi squared
  289. end
  292. %% Total fatigue estimate 3 (same coefficient for STfat Work and Rest, no LTfat)
  293. function [Chi,Fat,STfat,LTfat,Eff] = fat_one_noLT(p, E, fatigue_rating, effort)
  295. %% Regression coefficients
  296. alfa = p(1);
  297. delta = p(2);
  299. %% Empy arrays for scores
  300. STfat = nans(length(effort), 1);
  301. Fat = nans(length(effort), 1);
  302. LTfat = nans(length(effort), 1);
  303. Eff = nans(length(effort), 1);
  305. %% Starting fatigue values
  306. Fat_startp = 0.01;
  307. ST_fatigue_startp = 0;
  308. %%
  309. for t=1
  310. if effort(t) == 1
  311. STfat(t) = ST_fatigue_startp - (alfa*7.5);
  312. else
  313. STfat(t) = ST_fatigue_startp + (alfa*E(t)) - (alfa*2.5);
  314. end
  316. % Set limits to ST fatigue estimate
  317. if STfat(t) < 0
  318. STfat(t) = 0;
  319. end
  320. % Estimate total fatigue at time point t
  321. Fat(t) = Fat_startp + STfat(t);
  323. % Estimate effort at time point t
  324. if effort(t) == 1
  325. Eff(t) = 0;
  326. else
  327. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  328. end
  329. end
  331. for t=2:length(effort)
  332. if effort(t) == 1
  333. STfat(t) = STfat(t-1) - (alfa*7.5);
  334. else
  335. STfat(t) = STfat(t-1) + (alfa*E(t)) - (alfa*2.5);
  336. end
  338. % Set limits to ST fatigue estimate
  339. if STfat(t) < 0
  340. STfat(t) = 0;
  341. end
  342. % Estimate total fatigue at time point t
  343. Fat(t) = Fat_startp + STfat(t);
  345. % Estimate effort at time point t
  346. if effort(t) == 1
  347. Eff(t) = 0;
  348. else
  349. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  350. end
  351. end
  352. %% Fit measures
  353. residual_squares = ((fatigue_rating - Eff).^2);
  354. Chi = sum(residual_squares); % Chi squared
  356. end
  359. %% Total fatigue estimate 4 (same coefficients for STfat Work and Rest, another for LTfat)
  360. function [Chi,Fat,STfat,LTfat,Eff] = fat_onepar_withLT(p, E, fatigue_rating, effort)
  362. %% Regression coefficients
  363. alfa = p(1);
  364. gamma = p(2);
  365. delta = p(3);
  367. %% Empy arrays for scores
  368. STfat = nans(length(effort), 1);
  369. LTfat = nans(length(effort), 1);
  370. Fat = nans(length(effort), 1);
  371. Eff = nans(length(effort), 1);
  373. %% Starting fatigue values
  374. Fat_startp = 0.01;
  375. ST_fatigue_startp = 0;
  376. LT_fatigue_startp = 0;
  377. %%
  378. for t=1
  379. if effort(t) == 1
  380. STfat(t) = ST_fatigue_startp - (alfa*7.5);
  381. LTfat(t) = LT_fatigue_startp;
  382. else
  383. STfat(t) = ST_fatigue_startp + (alfa*E(t)) - (alfa*2.5);
  384. LTfat(t) = LT_fatigue_startp + (gamma*E(t));
  385. end
  387. % Set limits to ST fatigue estimate
  388. if STfat(t) < 0
  389. STfat(t) = 0;
  390. end
  391. % Estimate total fatigue at time point t
  392. Fat(t) = Fat_startp + STfat(t) + LTfat(t);
  394. % Estimate effort at time point t
  395. if effort(t) == 1
  396. Eff(t) = 0;
  397. else
  398. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  399. end
  400. end
  402. for t=2:length(effort)
  403. if effort(t) == 1
  404. STfat(t) = STfat(t-1) - (alfa*7.5);
  405. LTfat(t) = LTfat(t-1);
  406. else
  407. STfat(t) = STfat(t-1) + (alfa*E(t)) - (alfa*2.5);
  408. LTfat(t) = LTfat(t-1) + (gamma*E(t));
  409. end
  412. % Set limits to ST fatigue estimate
  413. if STfat(t) < 0
  414. STfat(t) = 0;
  415. end
  416. % Estimate total fatigue at time point t
  417. Fat(t) = Fat_startp + STfat(t) + LTfat(t);
  419. % Estimate effort at time point t
  420. if effort(t) == 1
  421. Eff(t) = 0;
  422. else
  423. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  424. end
  425. end
  426. %% Fit measures
  427. residual_squares = ((fatigue_rating - Eff).^2);
  428. Chi = sum(residual_squares); % Chi squared
  430. end
  433. %% Total fatigue estimate 5 (different coefficients for STfat Work and Rest, no LTfat)
  434. function [Chi,Fat,STfat,LTfat,Eff] = fat_noLT(p, E, fatigue_rating, effort)
  436. %% Regression coefficients
  437. alfa = p(1);
  438. beta = p(2);
  439. delta = p(3);
  441. %% Empy arrays for scores
  442. STfat = nans(length(effort), 1);
  443. LTfat = nans(length(effort), 1);
  444. Fat = nans(length(effort), 1);
  445. Eff = nans(length(effort), 1);
  447. %% Starting fatigue values
  448. Fat_startp = 0.01;
  449. ST_fatigue_startp = 0;
  450. %%
  451. for t=1
  452. if effort(t) == 1
  453. STfat(t) = ST_fatigue_startp - (alfa*7.5);
  454. else
  455. STfat(t) = ST_fatigue_startp + (beta*E(t)) - (alfa*2.5);
  456. end
  458. % Set limits to ST fatigue estimate
  459. if STfat(t) < 0
  460. STfat(t) = 0;
  461. end
  462. % Estimate total fatigue at time point t
  463. Fat(t) = Fat_startp + STfat(t);
  465. % Estimate effort at time point t
  466. if effort(t) == 1
  467. Eff(t) = 0;
  468. else
  469. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  470. end
  472. end
  474. for t=2:length(effort)
  475. if effort(t) == 1
  476. STfat(t) = STfat(t-1) - (alfa*7.5);
  477. else
  478. STfat(t) = STfat(t-1) + (beta*E(t)) - (alfa*2.5);
  479. end
  481. % Set limits to ST fatigue estimate
  482. if STfat(t) < 0
  483. STfat(t) = 0;
  484. end
  485. % Estimate total fatigue at time point t
  486. Fat(t) = Fat_startp + STfat(t);
  488. % Estimate effort at time point t
  489. if effort(t) == 1
  490. Eff(t) = 0;
  491. else
  492. Eff(t) = (E(t).*Fat(t)) + (E(t)*delta);
  493. end
  495. end
  496. %% Fit measures
  497. residual_squares = ((fatigue_rating - Eff).^2);
  498. Chi = sum(residual_squares); % Chi squared
  500. end
  503. %% Total fatigue estimate 6 (no fatigue, one parameter)
  504. function [Chi,Fat,STfat,LTfat,Eff] = noFat_onePara(p, E, fatigue_rating, effort)
  506. %% Regression coefficients
  507. alfa = p(1);
  509. %% Empy arrays for scores
  510. STfat = nans(length(effort), 1);
  511. LTfat = nans(length(effort), 1);
  512. Fat = nans(length(effort), 1);
  513. Eff = nans(length(effort), 1);
  515. %%
  516. for t=1:length(effort)
  518. if effort(t) == 1
  519. Eff(t) = 0;
  520. else
  521. Eff(t) = E(t)*alfa;
  522. end
  524. end
  527. %% Fit measures
  528. residual_squares = ((fatigue_rating - Eff).^2);
  529. Chi = sum(residual_squares); % Chi squared
  531. end
  534. end

ModellingCode_Experiment1_MullerEtAl2026CABN.m, no license · at the source

Overview

Authors: Tanja Müller1,2,3, Joseph Milton1, Masud Husain1,2,4, Matthew A J Apps1,2,5,6
ORCID iDs: Tanja Müller, Matthew A J Apps
  1. Department of Experimental Psychology, University of Oxford, Oxford, UK
  2. Wellcome Centre for Integrative Neuroimaging, University of Oxford, Oxford, UK
  3. Zurich Center for Neuroeconomics, Department of Economics, University of Zurich, Zurich, Switzerland
  4. Nuffield Department of Clinical Neurosciences, University of Oxford, Oxford, UK
  5. Centre for Human Brain Health, School of Psychology, University of Birmingham, Birmingham, UK
  6. Institute for Mental Health, School of Psychology, University of Birmingham, Birmingham, UK
Institutions: University of Zurich (Switzerland); University of Oxford (United Kingdom); Wellcome Centre for Integrative Neuroimaging (United Kingdom); University of Birmingham (United Kingdom)
Journal: Cognitive, affective & behavioral neuroscience, volume 26, issue 2, pages 650-668
Dates: received 5 June 2025; accepted 21 January 2026; published online 9 March 2026; in print 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.3758/s13415-026-01417-1 · PMID 41803422 · PMCID PMC13095941 · OpenAlex W7134838756
Open access: hybrid, a free copy (OpenAlex)
Status: code verified
Categories: computational modeling (no new data) (modality), human (organism)
Methods: Preprocessing, Statistics
Keywords: Physical exertion, Effort, Fatigue, Motivation, Reward, Computational model
MeSH: Fatigue*, Perception*, Physical Exertion*, Rest*, Adult, Computer Simulation, Female, Hand Strength, Humans, Male, Motivation, Reward, Young Adult (* major topic)
Topic: Motor Control and Adaptation (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Wellcome Trust (098282/Z/12/Z, 206330/Z/17/Z, 226645/Z/22/Z); Biotechnology and Biological Sciences Research Council (BB/M013596/1, BB/R010668/2, BB/R010668/1); Swiss National Science Foundation (217276, TMPFP1_217276); Studienstiftung des Deutschen Volkes; British Federation of Women Graduates; Jacobs Foundation; European Research Council
Citations: not cited yet (Europe PMC); 71 references in the paper

Abstract

Everyday we perform tasks that make us feel fatigued. Theoretical accounts predict that fatigue not only develops due to exertion of effort but also increases how effortful the same action will feel subsequently. However, to date there has been no formalised computational account of subjective perceptions of fatigue and effort, with few studies measuring these sensations directly or quantifying their moment-to-moment changes. In this study, across three experiments, participants were required to exert different levels of physical effort (grip force below maximum capacity) to obtain rewards, rating on each trial how effortful they found exerting force (Experiment 1) or how fatigued they felt (Experiments 2 and 3). Across studies, ratings of fatigue and perception of effort increased over time but also fluctuated on a trial-by-trial basis as a function of both effort exerted and rest. A computational model of fatigue, comprising a recoverable component (with fatigue reducing during rest) and an unrecoverable one (in which it only increases through effort exerted) successfully accounted for subjective responses. It was best able to explain momentary changes in both fatigue and effort perception. This computational model provides insights into the brain mechanisms underpinning the close, dynamic relationship between sensations of fatigue and effort.

Supplementary Information: The online version contains supplementary material available at 10.3758/s13415-026-01417-1.

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

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OSF sb9jf

License: none: the authors keep all their rights
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Languages: MATLAB (2)
Size: 2 files, 2 scripts
Software Heritage: not checked
Found in: “Code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Availability: 1 check, the latest on 30 September 2026: the link answers (HTTP 200)
  • 30 September 2026: the link answers (HTTP 200)
2 files
At the source: osf.io/sb9jf/

Code availability

Custom code is available on OSF (https://osf.io/sb9jf/; Digital Object Identifier: 10.17605/OSF.IO/SB9JF).

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

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.

What the map holds:

  • 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;
  • neither the text of the paper nor the code itself.

Its JSON (tracing-map.json) is deposited on Zenodo with its DOI once the map is validated.

Data

Datasets cited

Data availability

Data are available on the Open Science Framework (OSF; https://osf.io/v2dzq/; Digital Object Identifier: 10.17605/OSF.IO/V2DZQ). The study was not preregistered.

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

Versions

The history of this record: each version stored by the harvester or made by a correction of its authors or of the maintainers of its code, and what changed in its facts. The texts of the paper (its abstract, its availability statements) are not part of it; versions that changed only those are not listed.

Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 4 authors, 6 keywords, 13 MeSH terms, 7 funders, 67 references.

Cite

This paper

Müller, T., Milton, J., Husain, M., & Apps, M. A. J. (2026). Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue. Cognitive, affective & behavioral neuroscience, 26(2), 650-668. https://doi.org/10.3758/s13415-026-01417-1

BibTeX

@article{muller2026computational,
author = {Müller, Tanja and Milton, Joseph and Husain, Masud and Apps, Matthew A J},
title = {{Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue}},
journal = {Cognitive, affective \& behavioral neuroscience},
year = {2026},
month = mar,
volume = {26},
number = {2},
pages = {650--668},
publisher = {Springer Science+Business Media},
issn = {1530-7026},
doi = {10.3758/s13415-026-01417-1},
url = {https://doi.org/10.3758/s13415-026-01417-1},
pmid = {41803422},
pmcid = {PMC13095941}
}

RIS

TY - JOUR
AU - Müller, Tanja
AU - Milton, Joseph
AU - Husain, Masud
AU - Apps, Matthew A J
TI - Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue
T2 - Cognitive, affective & behavioral neuroscience
J2 - Cogn Affect Behav Neurosci
PY - 2026
DA - 2026/03/09
VL - 26
IS - 2
SP - 650
EP - 668
SN - 1530-7026
PB - Springer Science+Business Media
DO - 10.3758/s13415-026-01417-1
UR - https://doi.org/10.3758/s13415-026-01417-1
LA - en
ER -

CSL-JSON

{
"id": "10.3758/s13415-026-01417-1",
"type": "article-journal",
"title": "Computational signatures of exertion and rest underlie moment-to-moment dynamics of subjective perceptions of effort and fatigue",
"container-title": "Cognitive, affective & behavioral neuroscience",
"author": [
{
"family": "Müller",
"given": "Tanja"
},
{
"family": "Milton",
"given": "Joseph"
},
{
"family": "Husain",
"given": "Masud"
},
{
"family": "Apps",
"given": "Matthew A J"
}
],
"container-title-short": "Cogn Affect Behav Neurosci",
"volume": "26",
"issue": "2",
"page": "650-668",
"DOI": "10.3758/s13415-026-01417-1",
"PMID": "41803422",
"PMCID": "PMC13095941",
"ISSN": "1530-7026",
"publisher": "Springer Science+Business Media",
"URL": "https://doi.org/10.3758/s13415-026-01417-1",
"language": "en",
"issued": {
"date-parts": [
[
2026,
3,
9
]
]
}
}

The tracing map gets a citation of its own once an author has validated it and it has a DOI.

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