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The influence of nonlinear resonance on human cortical oscillations.

Code ↔ Paper

5 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 5 matches
  1. [1] § Materials and methods › Method › Test for Gaussianity and linearity through higher-order spectrum › Estimation of the Effective Number of Segments ↔ utility/fit_best_ar.m, lines 94–119 · score 0.67 · Corrected Akaike Information, AR model, AICc, Fit
  2. [2] § Materials and methods › Method › BiSpectral EEG Component Analysis (BiSCA) ↔ package/HoXiAlpha/@BiXiAlpha/init_para.m, lines 1–127 · score 0.61 · Levenberg Marquardt, algorithm, iteratively, optimal, squares, fitting
  3. [3] § Materials and methods › Method › Test for Gaussianity and linearity through higher-order spectrum › Median-Based Test for Gaussianity ↔ utility/calc_bc_stat.m, lines 85–142 · score 0.61 · asymptotic variance, population median, chi
  4. [4] § Results › Nonlinear resonances manifest in Rho peaks, while the Xi process remains linear and Gaussian at the bispectral (quadratic) level ↔ example/BiSCA/fig4_spatial_distribution.m, lines 96–192 · score 0.55 · nonlinearity statistic, Gaussianity statistic, compression, histograms, energy, Scatter
  5. [5] § Results › Simulation illustrating asymmetric waveforms and quadratic nonlinearity ↔ utility/nar_lpr_forecast.m, lines 1–133 · score 0.55 · state vectors, principal components, PC3, PC1, PC2, PCA

Paper

Loaded from Europe PMC by your browser, not stored by OSCR: doi.org · Europe PMC

The paper is loaded when this pane is shown.

The authors' code

MATLAB · 119 lines · 3.3 KB · GPL-3.0 · 1 match

  1. function armodel = fit_best_ar(y, Nlag, method)
  2. % FIT_BEST_AR Fits AR models of different orders to data y and selects the best model based on AICc
  3. %
  4. % armodel = FIT_BEST_AR(y, Nlag, method)
  5. %
  6. % Inputs:
  7. % y - Time series data (vector)
  8. % Nlag - Vector of AR model orders to try
  9. % method - (Optional) Method to estimate AR parameters. Options are:
  10. % 'arburg' - Uses Burg's method
  11. % 'levinson' - Uses Levinson-Durbin recursion (default)
  12. %
  13. % Output:
  14. % armodel - Struct containing the best AR model (fields: A, e)
  15. %
  17. % Set default method to 'levinson' if not provided
  18. if nargin < 3
  19. method = 'levinson';
  20. end
  22. % Ensure y is a column vector
  23. if size(y, 2) > 1
  24. y = y(:);
  25. end
  27. N = length(y);
  29. % Ensure Nlag is a column vector and sort in ascending order
  30. Nlag = Nlag(:);
  31. Nlag = sort(Nlag);
  33. % Convert y to double if it's single precision
  34. if isa(y, 'single')
  35. y = double(y);
  36. end
  38. % Initialize models cell array
  39. models = cell(length(Nlag), 1);
  41. % Start timing
  42. tic
  44. % Select method to compute AR parameters
  45. switch lower(method)
  46. case 'arburg'
  47. % Use Burg's method
  48. for i = 1:length(Nlag)
  49. p = Nlag(i);
  50. [A, E] = arburg(y, p);
  51. models{i}.A = A; % Normalized AR coefficients (leading 1)
  52. models{i}.e = E; % Estimated white noise variance
  53. end
  55. case 'levinson'
  56. % Use Levinson-Durbin recursion
  57. % Compute autocorrelation sequence once up to maximum lag
  58. maxLag = max(Nlag);
  59. r_full = xcorr(y, maxLag, 'biased');
  60. % Extract positive lags (from lag 0 to maxLag)
  61. r = r_full(maxLag + 1:end);
  63. for i = 1:length(Nlag)
  64. p = Nlag(i);
  65. % Apply Levinson-Durbin recursion
  66. [A, E] = levinson(r(1:p + 1), p);
  67. models{i}.A = A; % AR coefficients
  68. models{i}.e = E; % Prediction error (variance of white noise input)
  69. end
  71. otherwise
  72. error('Unknown method "%s". Options are "arburg" or "levinson".', method);
  73. end
  75. % End timing
  76. t = toc;
  77. fprintf('Fitting AR models took %f seconds\n', t);
  79. % Compute AICc for each model
  80. V = nan(length(Nlag), 1);
  82. for i = 1:length(Nlag)
  83. V(i) = araicc(models{i}, N);
  84. end
  86. % Select the model with minimum AICc
  87. [~, I] = min(V);
  88. armodel = models{I};
  89. fprintf('Choose order %f \n', Nlag(I));
  91. end
  93. % AICc computation function
  94. function v = araicc(model, N)
  95. % ARAICC Computes the corrected Akaike Information Criterion (AICc) for an AR model
  96. %
  97. % v = ARAICC(model, N)
  98. %
  99. % Inputs:
  100. % model - Struct containing AR model parameters (fields: A, e)
  101. % N - Length of the data used to fit the model
  102. %
  103. % Output:
  104. % v - AICc value
  105. %
  107. p = length(model.A) - 1; % Model order
  108. k = p + 1; % Number of parameters (AR coefficients + variance)
  110. % Log-likelihood
  111. LL = -0.5 * N * log(model.e);
  113. % Akaike Information Criterion
  114. AIC = 2 * k - 2 * LL;
  116. % Corrected AIC
  117. v = AIC + (2 * k * (k + 1)) / (N - k - 1);
  119. end

fit_best_ar.m at commit e98bac6, under GPL-3.0 · at the source

Overview

Authors: Ying Wang1, Min Li2, Ronaldo García Reyes1,3, Maria L. Bringas-Vega1,3, Ludovico Minati1,4, Michael Breakspear5, Pedro A. Valdes-Sosa1,3
ORCID iDs: Ying Wang, Min Li, Ronaldo García Reyes, Maria L. Bringas-Vega, Ludovico Minati, Michael Breakspear, Pedro A. Valdes-Sosa
  1. China-Cuba Belt and Road Joint Laboratory on Neurotechnology and Brain-Apparatus Communication, University of Electronic Science and Technology of China,Chengdu, China
  2. Hangzhou Dianzi University,Hangzhou, Zhejiang China
  3. Cuban Neuroscience Center,Havana, Cuba
  4. Center for Mind/Brain Sciences (CIMeC), University of Trento,Trento, Italy
  5. School of Science, College of Engineering, Science and the Environment, University of Newcastle,Newcastle, New South Wales Australia
Institutions: University of Electronic Science and Technology of China (China); Hangzhou Dianzi University (China); Cuban Neuroscience Center (Cuba); University of Trento (Italy); University of Newcastle Australia (Australia)
Journal: Communications biology, volume 9, issue 1, article 605
Dates: received 19 November 2025; accepted 21 April 2026; published online 4 May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1038/s42003-026-10164-5 · PMID 42082700 · PMCID PMC13144324 · OpenAlex W7160211861
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: EEG (modality), human (organism)
Methods: Spectral & time-frequency, Preprocessing, Statistics, Connectivity, Physiology & signal measures
Keywords: Dynamical systems, Oscillators, Signal processing, Electroencephalography - EEG, Nonlinear dynamics
MeSH: Cerebral Cortex*, Electroencephalography*, Nonlinear Dynamics*, Adult, Female, Humans, Male, Young Adult (* major topic)
Topic: Neural dynamics and brain function (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: National Natural Science Foundation of China (National Science Foundation of China) (W2411084); National Health and Medical Research Council (APP2008612)
Citations: cited by 4 papers (Europe PMC); 86 references in the paper

Abstract

Whether macroscale brain signals reflect linear or nonlinear organization remains poorly characterized. This distinction matters for modeling neural dynamics and interpreting oscillatory biomarkers of cognition and disease. Spectral analysis reveals aperiodic broadband and rhythmic narrowband components but does not capture nonlinear resonance, such as quadratic phase coupling among oscillations, which requires higher-order spectral analysis. We introduce BiSpectral EEG Component Analysis (BiSCA), combining spectral and bispectral analysis to separate aperiodic (Xi) from rhythmic (Rho) components, localize nonlinear signatures, and distinguish nonlinearity from non-Gaussianity; simulations confirm this separation. Applying BiSCA to two large datasets (1771 intracranial channels; 960 scalp EEG subjects), we detect significant nonlinear or non-Gaussian structure in 81.6% of scalp EEG and 67.9% of iEEG channels; forward modeling indicates the higher scalp prevalence reflects volume-conduction spread of focal nonlinear sources. In spatially focal iEEG, aperiodic Xi shows no detectable quadratic nonlinearity or non-Gaussianity, whereas Rho components, including Alpha and Mu, carry the dominant cortical quadratic coupling. Despite higher occipital Alpha power, the strongest nonlinear signatures arise from parietal Mu. Nonlinear resonance is thus expressed primarily through oscillatory rather than aperiodic dynamics.

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

Repositories

Its files are read in the Code ↔ Paper reader above, with 5 matches between paragraphs and lines of code.

rigelfalcon/BiSCA

License: GPL-3.0
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: e98bac6abfc993d82c281628ae6891f86ee3886c, 18 April 2026
Languages: MATLAB (233), Shell (1)
Size: 240 files, 234 scripts
Software Heritage: not archived
Found in: “Code availability”
Holds: README, license file, CITATION.cff
Not found: environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (13 files), Parallel Computing Toolbox (12 files), Signal Processing Toolbox (5 files), EEGLAB (3 files), Brainstorm (1 file), FieldTrip (1 file), Optimization Toolbox (1 file), Violinplot-Matlab (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
236 files
At the source: github.com/rigelfalcon/BiSCA

Zenodo 19643376

License: GPL-3.0
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Size: 1 file
Software Heritage: not checked
Found in: “Code availability”
Not found: README, license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Statistics and Machine Learning Toolbox (13 files), Parallel Computing Toolbox (12 files), Signal Processing Toolbox (5 files), EEGLAB (3 files), Brainstorm (1 file), FieldTrip (1 file), Optimization Toolbox (1 file), Violinplot-Matlab (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers (HTTP 200)
  • 28 September 2026: the link answers (HTTP 200)
236 files
At the source:

Code availability

The analysis code and derived data used in this study are publicly available on GitHub at https://github.com/rigelfalcon/BiSCA and Zenodo 10.5281/zenodo.1964337686.

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:

  • 2 repositories of the authors' code, each at its verified commit, with its license and how the link was found in the paper;
  • 468 scripts, each with its path and the digest of its content;
  • 5 matches between paragraphs of the paper and lines of the code (method lexical-v1);
  • 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

The scalp EEG and intracranial EEG (iEEG) data analyzed in this study were obtained from the work of Li et al.71 (https://www.synapse.org/Synapse:syn26712693/wiki/) and Frauscher et al.59 (https://ieegatlas.loris.ca/), respectively. Ethical approval was not required for this specific study as it exclusively analyzed pre-existing, publicly available, and anonymized datasets (the HarMNqEEG dataset and the Montreal Neurological Institute (MNI) open iEEG atlas). The collection of the original data received ethical approval from the respective local authorities, as detailed in the original publications59,71.

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, 28 September 2026: the first record

Recorded: type, language, journal, volume, issue, pages, dates, 7 authors, 5 keywords, 8 MeSH terms, 2 funders, 77 references.

Cite

This paper

Wang, Y., Li, M., García Reyes, R., Bringas-Vega, M. L., Minati, L., Breakspear, M., & Valdes-Sosa, P. A. (2026). The influence of nonlinear resonance on human cortical oscillations. Communications biology, 9(1), 605. https://doi.org/10.1038/s42003-026-10164-5

BibTeX

@article{wang2026influence,
author = {Wang, Ying and Li, Min and García Reyes, Ronaldo and Bringas-Vega, Maria L. and Minati, Ludovico and Breakspear, Michael and Valdes-Sosa, Pedro A.},
title = {{The influence of nonlinear resonance on human cortical oscillations}},
journal = {Communications biology},
year = {2026},
month = may,
volume = {9},
number = {1},
pages = {605},
publisher = {Nature Publishing Group},
issn = {2399-3642},
doi = {10.1038/s42003-026-10164-5},
url = {https://doi.org/10.1038/s42003-026-10164-5},
pmid = {42082700},
pmcid = {PMC13144324}
}

RIS

TY - JOUR
AU - Wang, Ying
AU - Li, Min
AU - García Reyes, Ronaldo
AU - Bringas-Vega, Maria L.
AU - Minati, Ludovico
AU - Breakspear, Michael
AU - Valdes-Sosa, Pedro A.
TI - The influence of nonlinear resonance on human cortical oscillations
T2 - Communications biology
J2 - Commun Biol
PY - 2026
DA - 2026/05/04
VL - 9
IS - 1
SP - 605
SN - 2399-3642
PB - Nature Publishing Group
DO - 10.1038/s42003-026-10164-5
UR - https://doi.org/10.1038/s42003-026-10164-5
LA - en
ER -

CSL-JSON

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