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Learning the bistable cortical dynamics of the sleep-onset period.

Code ↔ Paper

9 matches between paragraphs of the paper and lines of its authors' code, computed by the harvester (lexical-v1). Click a colored paragraph or line to see its counterpart.

The 9 matches · 4 of them tie a paragraph to a whole file without given lines: weak matches, whose lines are not tinted
  1. [1] § Materials and methods › EEG recordings ↔ code/step1_embedding.m, the whole file · a weak match · score 0.70 · pass filter, alpha band, transform, cmor1, bins, wavelet · Report a mismatch
  2. [2] § Materials and methods › EEG recordings ↔ plots/fig2_embedding.m, lines 1 to 41 · score 0.63 · alpha band, embedding extraction, cmor1, bins, wavelet, EEG · Report a mismatch
  3. [3] § Materials and methods › Dataset ↔ plots/fig8_corr.py, lines 1 to 26 · score 0.62 · Sleepiness Scale, sleep scales, Karolinska, KSS, Stanford, nap · Report a mismatch
  4. [4] § Materials and methods › SOP window definition ↔ plots/fig10_comp_mode.m, the whole file · a weak match · score 0.61 · delta band, alpha band, window, ratio, wavelet, amplitudes · Report a mismatch
  5. [5] § Materials and methods › SOP window definition ↔ code/step1_embedding.m, the whole file · a weak match · score 0.60 · delta band, alpha band, ratio, wavelet, amplitudes, spectrograms · Report a mismatch
  6. [6] § Results › The bistable characteristics of the SOP are preserved in a low-rank embedding of the EEG spectrogram ↔ plots/fig2_embedding.m, lines 104 to 181 · score 0.58 · SOP spectrogram, low dimensional, sleep mode, embedding, EEG, wake · Report a mismatch
  7. [7] § Materials and methods › Embedding extraction ↔ plots/fig2_embedding.m, lines 104 to 181 · score 0.54 · SOP spectrogram, low dimensional, gaussian, embedding, wake, EEG · Report a mismatch
  8. [8] § Materials and methods › Model evaluation › Per-timepoint likelihood. ↔ code/step2_param_est.py, lines 37 to 74 · score 0.52 · Euler Maruyama, cubic SDE, Gaussian · Report a mismatch
  9. [9] § Results › The bistable characteristics of the SOP are preserved in a low-rank embedding of the EEG spectrogram ↔ plots/fig10_comp_mode.m, the whole file · a weak match · score 0.51 · alpha band, transitional period, dominant, window, amplitude, 100 s · Report a mismatch

Paper

Loaded from Europe PMC by your browser; OSCR does not store it: doi.org · Europe PMC

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The authors' code

MATLAB · 201 lines · 6.1 KB · MIT · 3 matches

  1. %% Embedding extraction (sub 9)
  2. clc,clear all;close all;
  3. embed_folder = ['..\data\EEG\'];
  4. ls = dir([embed_folder,'ds*mat']);
  5. % Focus on first 30 minutes
  6. fs = 100;
  7. t_start = 1*fs;
  8. t_end = 1800*fs;
  9. t = linspace(t_start,t_end,(t_end - t_start + 1)) / fs;
  10. % Wavelet parameter
  11. wavelet_name = 'cmor1-1.5';
  12. central_freq = centfrq(wavelet_name);
  13. freq_start = 0.5;
  14. freq_end = 20;
  15. num_bin = 200;
  16. w = linspace(freq_start,freq_end,num_bin)';
  17. scales = (central_freq/(1/fs))./w;
  18. % Define frequency band of interests
  19. delta_band = find( 0.5 < w & w < 4);
  20. alpha_band = find( 8 < w & w < 12);
  21. % Plot settings
  22. figure('Position',1.0e+03*[ 0.1106 0.1778 1.2712 0.4842]);
  23. fig = figure('Position',[441.0000 125.0000 586.4000 503.2000]);
  24. for k = 1:3
  25. axe{k} = axes('Position',[0.15,0.1+0.27*(k-1),0.7,0.18]);
  26. end
  27. axe{4} = axes('Position',[0.03,0.1+0.27*(2-1),0.05,0.18]);
  28. axe{5} = axes('Position',[0.92,0.1+0.27*(2-1),0.05,0.18]);
  29. % Load sample subject
  30. s_idx = 9;
  31. data_file = [embed_folder,ls(s_idx).name];
  32. load(data_file);
  33. data = squeeze(data(:,1,:,:,:,t_start:t_end));
  34. % Take the Wavelt representation
  35. amp_wav = abs(cwt(data',scales,wavelet_name));
  36. % Decide the transition window
  37. amp_ratio = sum(amp_wav(delta_band,:),1) ./ sum(amp_wav(alpha_band,:),1);
  38. sm_ratio= smoothdata(amp_ratio,"gaussian",300);
  39. % 3 min larger than 1
  40. thres_start = 1;
  41. dur_tran_start = 60*fs;
  42. cond = sm_ratio > thres_start;
  43. % Find the start and end indices of consecutive true sequences
  44. d = diff([0, cond, 0]);
  45. % This finds the start and the end of transition period
  46. run_starts = find(d == 1);
  47. run_ends = find(d == -1);
  48. % Calculate the durations of the runs
  49. run_dur = run_ends - run_starts + 1; % Length in samples
  50. req_run_idx = find(run_dur >= dur_tran_start);
  51. t_transtart = run_starts(req_run_idx(1));
  52. thres_end = 1;
  53. dur_tran_end = 120*fs;
  54. cond = sm_ratio > thres_end;
  55. % Find the start and end indices of consecutive true sequences
  56. d = diff([0, cond, 0]);
  57. % This finds the start and the end of transition period
  58. run_starts = find(d == 1);
  59. run_ends = find(d == -1);
  60. % Calculate the durations of the runs
  61. run_dur = run_ends - run_starts + 1; % Length in samples
  62. req_run_idx = find(run_dur >= dur_tran_end);
  63. t_tranend = run_starts(req_run_idx(1));
  64. t_ana = [t_transtart-200*fs, t_tranend+200*fs];
  65. % Extract dominant mode in wake and sleep state
  66. if t_ana(1) < 0
  67. wav_ana = amp_wav(:,[1:t_ana(2)]);
  68. t_ana_win = [1:t_ana(2)]/fs;
  69. else
  70. wav_ana = amp_wav(:,[t_ana(1):t_ana(2)]);
  71. t_ana_win = [t_ana(1):t_ana(2)]/fs;
  72. end
  73. % Dominant mode in wake state
  74. wav_wake = wav_ana(:,1:60*fs);
  75. [Uw,Sw,Vw] = svd(wav_wake,'econ');
  76. wav_sleep = wav_ana(:,(end-60*fs):end);
  77. [Us,Ss,Vs] = svd(wav_sleep,'econ');
  78. if Uw(:,1) < 0
  79. mode_wake = -1*Uw(:,1);
  80. else
  81. mode_wake = Uw(:,1);
  82. end
  83. if Us(:,1) < 0
  84. mode_sleep = -1*Us(:,1);
  85. else
  86. mode_sleep = Us(:,1);
  87. end
  88. % Extract the low_dimensional dynamics
  89. wav_norm = wav_ana ./ vecnorm(wav_ana, 2, 1);
  90. mu = (wav_norm-mode_sleep)'*(mode_wake-mode_sleep) / norm(mode_wake - mode_sleep,2).^2;
  91. mu = smoothdata(mu,"gaussian",100);
  92. gca = axe{3};
  93. sm_wav = smoothdata(abs(wav_ana),2,"gaussian",300);
  94. hdl = imagesc(gca,t_ana_win,w, sm_wav);hold(gca,"on");
  95. hdl.Parent.YDir = 'normal';
  96. colormap turbo;
  97. set(gca,'clim',[-8,30]);
  98. set(gca,'ylim',[1,15]);
  99. ylabel('Frequency [Hz]');
  100. set(gca,'xlim',[t_ana_win(1),t_ana_win(end)]);
  101. hold(gca,'on');
  102. ylim = get(gca,'ylim');
  103. t_end = t(run_starts(req_run_idx(1)))+ 2*60;
  104. wake_time = [t_ana_win(1),t_ana_win(1)+60];
  105. sleep_time = [t_ana_win(end)-60,t_ana_win(end)];
  106. area(gca,wake_time, [15, 15], 'FaceColor', 'blue', 'FaceAlpha', 0.3);
  107. area(gca,sleep_time, [15, 15], 'FaceColor', 'blue', 'FaceAlpha', 0.3);
  108. set(gca, 'XTick', []);
  109. title(gca,'EEG SOP Spectrogram','FontSize',10);
  110. ylabel(gca,'Frequency [Hz]','FontSize',10);
  111. text(gca,0.06, 0.3, ["Wake"], 'Units', 'normalized',...
  112. 'FontSize', 11, 'Color', 'k', 'HorizontalAlignment', 'center');
  113. text(gca,0.94, 0.8, ["Sleep"], 'Units', 'normalized',...
  114. 'FontSize', 11, 'Color', 'k', 'HorizontalAlignment', 'center');
  115. gca = axe{1}
  116. mu_scale = (mu - min(mu)) ./ (max(mu) - min(mu));
  117. recon_spec = mode_wake*mu_scale'+ mode_sleep*(1-mu_scale)';
  118. sm_recon = smoothdata(recon_spec,2,'gaussian',300);
  119. hdl = imagesc(gca,t_ana_win,w,recon_spec); %
  120. hdl.Parent.YDir = 'normal';
  121. colormap turbo;
  122. set(gca,'ylim',[1,15]);
  123. set(gca,'fontsize',10);
  124. title(gca,'Reconstruction (\mu(t)U_w^{1}+(1-\mu(t))U_s^{1})','FontSize',10);
  125. xlabel(gca,'Time [s]');
  126. set(gca,'clim',[0,0.15]);
  127. ylabel(gca,'Frequency [Hz]','FontSize',10);
  128. gca = axe{2};
  129. plot(gca,t_ana_win,mu);
  130. set(gca,'xlim',[t_ana_win(1),t_ana_win(end)]);
  131. set(gca, 'XTick', []);
  132. title(gca,'\mu(t) (projection on U_w^{1}-U_s^{1})','FontSize',10);
  133. set(gca,'fontsize',10);
  134. % Plot two patches for the wake and sleep mode
  135. dummy_width = 5;
  136. mode_wake_patch = repmat(mode_wake, 1, dummy_width);
  137. mode_sleep_patch = repmat(mode_sleep, 1, dummy_width);
  138. % 3) Create a new axis for the wake mode patch
  139. gca = axe{4};
  140. imagesc(gca, 1:dummy_width, w, mode_wake_patch);
  141. set(gca, 'YDir','normal', 'XTick',[], 'YTick',[]);
  142. title(gca, 'U_w^{1}', 'FontSize', 9);
  143. colormap(gca, turbo); % Use the same colormap as your main spectrogram
  144. clim(gca, [0, 0.16]); % Match color limits if you want
  145. set(gca,'ylim',[1,15]);
  146. ylabel(gca,'Frequency [Hz]','FontSize',10);
  147. gca = axe{5};
  148. imagesc(gca, 1:dummy_width, w, mode_sleep_patch);
  149. set(gca, 'YDir','normal', 'XTick',[], 'YTick',[]);
  150. title(gca, 'U_s^{1}', 'FontSize', 9);
  151. colormap(gca, turbo); % Use the same colormap as your main spectrogram
  152. clim(gca, [0, 0.16]); % Match color limits if you want
  153. set(gca,'ylim',[1,15]);
  154. set(gca,'xlim',[1,5]);
  155. ylabel(gca,'Frequency [Hz]','FontSize',10);
  156. saveas(gcf,'..\figures\fig2a_sample_embedding.png');
  157. %% Plot all embeddings
  158. clc,clear all;close all;
  159. folder = ['../embedding/'];
  160. figure('Position', 1.0e+03 * [0.1146 0.1074 1.2304 0.5408]);
  161. ls = dir([folder,'*.mat']);
  162. fs = 10;
  163. for f_idx = 1:length(ls)
  164. filename = [folder,ls(f_idx).name];
  165. load(filename);
  166. subplot(4,5,f_idx);
  167. t = [1:length(ds_mu)]/fs;
  168. plot(t,ds_mu);
  169. tit = ['sub',num2str(f_idx)];
  170. title(tit);
  171. set(gca,'xlim',[t(1),t(end)]);
  172. set(gca,'fontsize',10)
  173. end
  174. saveas(gcf,'..\figures\fig2b_all_embeddings.png');

fig2_embedding.m at commit 68d7750, under MIT · at the source

Overview

Authors: Zhenxing Hu1, Manaoj Aravind1, Xu Lei2, J. Nathan Kutz3, Jean-Julien Aucouturier1
  1. Department of Robotics and Control, Université Marie et Louis Pasteur, SUPMICROTECH, CNRS, institut FEMTO-ST, Besançon, France
  2. Faculty of Psychology, Sleep and Neuroimaging Center, Southwest University, Chongqing, China
  3. Department of Applied Mathematics and Electrical and Computer Engineering, University of Washington, Seattle, Washington, United States of America
Journal: PLoS computational biology, volume 22, issue 4, article e1014246
Dates: received 4 September 2025; accepted 17 April 2026; published online 30 April 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1371/journal.pcbi.1014246 · PMID 42060699 · PMCID PMC13152216 · OpenAlex W4412559431
Open access: gold, a free copy (OpenAlex)
Status: code verified (how the code is found and verified)
Categories: EEG (modality), human (organism), computational (subfield)
Methods: Spectral & time-frequency, Machine learning
MeSH: Cerebral Cortex*, Models, Neurological*, Sleep*, Sleep Stages*, Computational Biology, Computer Simulation, Electroencephalography, Humans, Stochastic Processes, Wakefulness (* major topic)
Journal subjects: Biology and Life Sciences, Physiology, Physiological Processes, Sleep, Research and Analysis Methods, Bioassays and Physiological Analysis, Electrophysiological Techniques, Brain Electrophysiology, Electroencephalography, Electrophysiology, Neurophysiology, Neuroscience, Brain Mapping, Medicine and Health Sciences, Clinical Medicine, Clinical Neurophysiology, Imaging Techniques, Neuroimaging, Computer and Information Sciences, Systems Science, Dynamical Systems, Physical Sciences, Mathematics, Probability Theory, Statistical Distributions, Algebra, Linear Algebra, Singular Value Decomposition, Simulation and Modeling, Engineering and Technology, Electronics Engineering, Electronics, Electrodes, Numerical Analysis, Interpolation
Topic: EEG and Brain-Computer Interfaces (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: MSCA Doctoral Network (LULLABYTE); Region Bourgogne Franche-Comté ANER (ASPECT); National Natural Science Foundation of China (32471095); ANR (ANR-17-EURE-0002); US National Science Foundation (NSF) (AI Institute for Dynamical Systems 2112085); Air Force Office of Scientific Research (FA9550-24-1-0141)
Citations: not cited yet (Europe PMC); 31 references in the paper

Abstract

Humans just don’t fall asleep like a log – or step-function. Rather, the sleep-onset period (SOP) exhibits dynamic and non-monotonous changes of electroencephalogram (EEG) with high, and so far poorly understood, intra- and inter-individual variability. Computational models of the sleep regulation network have suggested that the transition to sleep can be viewed as a noisy bifurcation at a saddle node which is determined by an underlying control signal or “sleep drive”. However, such models do not describe how internal control signals in the SOP can produce rapid switches between stable wake and sleep states, nor how these state-space changes are translated in the macroscopic EEG. Here, we propose a minimally-parameterized stochastic dynamical model, in which one slowly-varying control parameter drives the wake-to-sleep transition while exhibiting noise-driven bistability. We provide a procedure for estimating the parameters of the model given single observations of experimental sleep EEG data, and show that it can reproduce a wide variety of SOP phenomenology. Using the model to analyze a pre-existing sleep EEG dataset, we find that the estimated model parameters correlate with subjective sleepiness reports. These results suggest that the bistable characteristics of the SOP can serve as biomarkers for tracking intra- and inter-individual variability of sleep-onset disorders.

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

Repository

Its files are read in the Code ↔ Paper reader above, with 9 matches between paragraphs and lines of code.

neuro-team-femto/cubic_sleep

License: MIT
State: the link answers, verified on 30 September 2026
Evidence: files inventoried
Commit: 68d7750e35d2574894d579e2471a270b6da45daf, 20 January 2026
Languages: MATLAB (7), Python (5)
Size: 74 files, 12 scripts
Software Heritage: not archived
Found in: “Data Availability”
Holds: README, license file, environment (environment.yml)
Not found: CITATION.cff, tests, continuous integration, documentation
Tools: Wavelet Toolbox (4 files), Matplotlib (4 files), NumPy (4 files), SciPy (4 files), pandas (3 files), seaborn (3 files), Statistics and Machine Learning Toolbox (2 files), PyMC (2 files), ArviZ (1 file)
Availability: 1 check, the latest on 30 September 2026: the link answers
  • 30 September 2026: the link answers
14 files

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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  • 12 scripts, each with its path and the digest of its content;
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Data

No dataset and no data link were found in the paper.

Data Availability

Data availability preprocessed EEG data of 19 subjects are available at https://github.com/neuro-team-femto/cubic_sleep/tree/main/data/EEG (used for academic purposes under MIT license). Code availability for embedding extraction and parameter estimation is accessible on GitHub at https://github.com/neuro-team-femto/cubic_sleep/. The code for reproducing all the figures could be found at https://github.com/neuro-team-femto/cubic_sleep/tree/main/plots.

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

Versions

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Version 1, 30 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 5 authors, 10 MeSH terms, 6 funders, 28 references.

Cite

This paper

Hu, Z., Aravind, M., Lei, X., Kutz, J. N., & Aucouturier, J.-J. (2026). Learning the bistable cortical dynamics of the sleep-onset period. PLoS computational biology, 22(4), e1014246. https://doi.org/10.1371/journal.pcbi.1014246

BibTeX

@article{hu2026learning,
author = {Hu, Zhenxing and Aravind, Manaoj and Lei, Xu and Kutz, J. Nathan and Aucouturier, Jean-Julien},
title = {{Learning the bistable cortical dynamics of the sleep-onset period}},
journal = {PLoS computational biology},
year = {2026},
month = apr,
volume = {22},
number = {4},
pages = {e1014246},
publisher = {PLOS},
issn = {1553-734X},
doi = {10.1371/journal.pcbi.1014246},
url = {https://doi.org/10.1371/journal.pcbi.1014246},
pmid = {42060699},
pmcid = {PMC13152216}
}

RIS

TY - JOUR
AU - Hu, Zhenxing
AU - Aravind, Manaoj
AU - Lei, Xu
AU - Kutz, J. Nathan
AU - Aucouturier, Jean-Julien
TI - Learning the bistable cortical dynamics of the sleep-onset period
T2 - PLoS computational biology
J2 - PLoS Comput Biol
PY - 2026
DA - 2026/04/30
VL - 22
IS - 4
SP - e1014246
SN - 1553-734X
PB - PLOS
DO - 10.1371/journal.pcbi.1014246
UR - https://doi.org/10.1371/journal.pcbi.1014246
LA - en
ER -

CSL-JSON

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"id": "10.1371/journal.pcbi.1014246",
"type": "article-journal",
"title": "Learning the bistable cortical dynamics of the sleep-onset period",
"container-title": "PLoS computational biology",
"author": [
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"family": "Hu",
"given": "Zhenxing"
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"given": "Manaoj"
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{
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"container-title-short": "PLoS Comput Biol",
"volume": "22",
"issue": "4",
"page": "e1014246",
"DOI": "10.1371/journal.pcbi.1014246",
"PMID": "42060699",
"PMCID": "PMC13152216",
"ISSN": "1553-734X",
"publisher": "PLOS",
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}

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