OSCR

Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions.

Code ↔ Paper

2 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 2 matches · all tie a paragraph to a whole file, not to given lines: weak matches, whose lines are not tinted
  1. [1] § Materials and methods › Frequency scaling/warping ↔ gh_warpfrequency.m, the whole file · a weak match · score 0.91 · amplitude envelope, Hilbert transform, analytic signal, domain signal, analytic representations, instantaneous phase
  2. [2] § Materials and methods › Synchronization index between two univariate signals ↔ gh_warpfrequency.m, the whole file · a weak match · score 0.81 · Hilbert transform, narrow band, analytic representation, instantaneous phases, Cross frequency, filtered

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 · 114 lines · 3.4 KB · no license · 2 matches

  1. function x_warped = gh_warpfrequency(x, FrBase, factor, fs)
  2. % Copyright (C) 2026 Carmen Vidaurre
  4. % This program is free software: you can redistribute it and/or modify
  5. % it under the terms of the GNU General Public License as published by
  6. % the Free Software Foundation, either version 3 of the License, or
  7. % (at your option) any later version.
  9. % This program is distributed in the hope that it will be useful,
  10. % but WITHOUT ANY WARRANTY; without even the implied warranty of
  11. % MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the
  12. % GNU General Public License for more details
  14. %WARP_FREQUENCY Frequency-warp a narrow-band component of a multichannel signal.
  15. %
  16. % x_warped = gh_WARPFREQUENCY(x, FrBase, factor, fs)
  17. %
  18. % This function extracts a narrow band centered around a base frequency
  19. % (FrBase), computes its analytic representation, multiplies the
  20. % instantaneous phase by a given factor, and reconstructs a real-valued
  21. % warped signal. This effectively shifts/warps the component from
  22. % FrBase → FrBase * factor (approximately).
  23. %
  24. % INPUTS:
  25. % x - Time-domain signal, size [T × Nchannels]
  26. % FrBase - Base frequency of interest (Hz), e.g., 3 Hz
  27. % factor - Frequency multiplication factor, e.g., 2 → from 3 Hz to 6 Hz
  28. % fs - Sampling frequency (Hz)
  29. %
  30. % OUTPUT:
  31. % x_warped - Frequency-warped signal, same size as x
  32. %
  33. % EXAMPLE:
  34. % % Warp a 3 Hz oscillation to 6 Hz:
  35. % y = warp_frequency(x, 3, 2, fs);
  36. %
  37. % NOTE:
  38. % The method uses:
  39. % - narrow band-pass filtering
  40. % - analytic signal via Hilbert transform
  41. % - instantaneous phase multiplication
  42. %
  43. % Author: Carmen Vidaurre
  44. % Please cite: Vidaurre, C., Eguinoa, R., Maudrich, T. et al. Canonical coherence
  45. % for the estimation of within- and cross-frequency cortico-kinematic interactions.
  46. % Sci Rep 16, 15182 (2026).
  47. % https://doi.org/10.1038/s41598-026-49471-6
  48. % -------------------------------------------------------------------------
  50. %% -----------------------
  51. % Input validation
  52. % ------------------------
  53. if nargin < 4
  54. error('warp_frequency requires inputs: x, FrBase, factor, fs.');
  55. end
  56. if FrBase <= 0
  57. error('FrBase must be positive.');
  58. end
  59. if factor <= 0
  60. error('factor must be positive.');
  61. end
  62. if fs <= 0
  63. error('Sampling frequency fs must be positive.');
  64. end
  66. % Ensure column-oriented time dimension
  67. if size(x,1) < size(x,2)
  68. warning('Input x appears transposed. Expected [T × channels].');
  69. end
  72. %% -----------------------
  73. % Design narrow band-pass filter
  74. % ------------------------
  75. % Bandwidth: ±1 Hz around FrBase
  76. f_low = max(FrBase - 1, 0.1); % prevent 0 Hz edge
  77. f_high = FrBase + 1;
  79. % Normalize to Nyquist frequency
  80. Wn = [f_low f_high] / (fs/2);
  82. % 4th-order Butterworth BPF
  83. [b, a] = butter(2, Wn);
  86. %% -----------------------
  87. % Apply zero-phase band-pass filter
  88. % ------------------------
  89. % filtfilt ensures zero-phase distortion
  90. x_filt = filtfilt(b, a, x);
  93. %% -----------------------
  94. % Compute analytic signal using Hilbert transform
  95. % ------------------------
  96. x_analytic = hilbert(x_filt);
  99. %% -----------------------
  100. % Frequency warping
  101. % ------------------------
  102. % Warp = keep amplitude envelope |analytic|
  103. % but multiply instantaneous phase by `factor`
  104. %
  105. % analytic = A * exp(i * φ)
  106. % warped = A * exp(i * (factor * φ))
  108. A = abs(x_analytic); % this is the original envelope
  109. phi = angle(x_analytic);
  111. x_warped = real( A .* exp(1i * (factor .* phi)) );
  114. end

gh_warpfrequency.m at commit d31b277, no license · at the source

Overview

Authors: Carmen Vidaurre1,2,3, Rubén Eguinoa4, Tom Maudrich5, Rouven Kenville5, Nerea Irastorza-Landa6, Ricardo San Martín4, Vadim Nikulin7
ORCID iDs: Carmen Vidaurre
  1. Basque Center on Cognition, Brain and Language,Mikeletegi Pasealekua, 69, 20009 Donostia, Gipuzkoa Spain
  2. Ikerbasque, Euskadi Pl.,48009 Bilbo, Bizkaia Spain
  3. Department of Machine Learning, TU-Berlin,Marchstraße 23, 10587 Berlin, Germany
  4. Department of Ciencias, Universidad Publica de Navarra,Av. Cataluña, s/n, 31006 Pamplona, Navarra Spain
  5. Faculty of Sports Science, Department Movement Neuroscience, Leipzig University,04103 Leipzig, Germany
  6. Tecnalia Basque Research and Technology Alliance (BRTA),Mikeletegi Pasealekua, 2, 20009 Donostia, Gipuzkoa Spain
  7. Max Planck Institute for Human Cognitive and Brain Sciences,Stephanstraße 1A, 04103 Leipzig, Germany
Institutions: Basque Center on Cognition, Brain and Language (Spain); Ikerbasque (Spain); Technische Universität Berlin (Germany); Universidad Pública de Navarra (UPNA) (Spain); Leipzig University (Germany); Tecnalia (Spain); Max Planck Institute for Human Cognitive and Brain Sciences (Germany)
Journal: Scientific reports, volume 16, issue 1, article 15182
Dates: received 21 November 2025; accepted 15 April 2026; published online 15 May 2026
Type: Research article · Language: English
License: CC BY
Identifiers: DOI 10.1038/s41598-026-49471-6 · PMID 42140985 · PMCID PMC13179363 · OpenAlex W7161231371
Open access: gold, a free copy (OpenAlex)
Status: code verified
Categories: EEG (modality), other (modality), human (organism)
Methods: Spectral & time-frequency, Statistics, Smoothing, state filtering, decompositions, Connectivity, Physiology & signal measures
Keywords: Computational biology and bioinformatics, Engineering, Neuroscience
MeSH: Motor Cortex*, Biomechanical Phenomena, Computer Simulation, Electroencephalography, Humans, Movement (* major topic)
Topic: EEG and Brain-Computer Interfaces (Cognitive Neuroscience, Neuroscience), according to OpenAlex
Funding: Max Planck Institute for Human Cognitive and Brain Sciences (2)
Citations: cited by 1 paper (Europe PMC); 44 references in the paper

Abstract

Cortico-kinematic coherence (CKC) quantifies coupling between cortical activity and movement kinematics, serving as a non-invasive marker of sensorimotor integration and motor control. Conventional CKC approaches primarily assess within (linear) frequency coupling and overlook cross-frequency interactions, which are increasingly recognized as central to corticomuscular communication. We present a novel multivariate framework that extends the canonical coherence (caCOH) method by applying a non-linear warping of peripheral measures, enabling detection of cross-frequency CKC. The method jointly analyzes multichannel EEG and acceleration signals, maximizing sensitivity to spatially distributed neural sources while accounting for frequency-specific structure. Simulations with realistic head modeling show that the approach robustly recovers underlying patterns even at very low signal-to-noise ratios, closely matching the ground truth. Application to empirical EEG and acceleration data demonstrates that cross-frequency CKC is statistically significant in most participants and interaction pairs, indicating consistent non-random coupling. We further introduce an analysis strategy to determine whether observed interactions arise from shared (e.g. due to the signal shape) or distinct cortical sources. This framework provides a multivariate tool for characterizing the neural mechanisms of motor control and offers future opportunities for investigating their disruption in neurological 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 2 matches between paragraphs and lines of code.

CarmenVidaurre/cacoh

License: none: the authors keep all their rights
State: the link answers, verified on 28 September 2026
Evidence: files inventoried
Commit: d31b2773aefb2ec0e0e2c2e5acc021659e61f341, 2 September 2026
Languages: MATLAB (2)
Size: 3 files, 2 scripts
Software Heritage: not archived
Found in: “Data availability”
Holds: README
Not found: license file, CITATION.cff, environment file, tests, continuous integration, documentation
Tools: Signal Processing Toolbox (1 file)
Availability: 1 check, the latest on 28 September 2026: the link answers
  • 28 September 2026: the link answers
3 files
At the source: github.com/CarmenVidaurre/cacoh

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.

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;
  • 2 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

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

Data availability

Participants’ raw canonical coherence and cross-frequency canonical coherence values are available in the supporting material. Supporting codes to compute canonical coherence and signal warping are available at https://github.com/CarmenVidaurre/cacoh For further inquiries regarding the data or code, please contact one of the corresponding authors.

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, 3 keywords, 6 MeSH terms, 1 funder, 38 references.

Cite

This paper

Vidaurre, C., Eguinoa, R., Maudrich, T., Kenville, R., Irastorza-Landa, N., San Martín, R., & Nikulin, V. (2026). Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions. Scientific reports, 16(1), 15182. https://doi.org/10.1038/s41598-026-49471-6

BibTeX

@article{vidaurre2026canonical,
author = {Vidaurre, Carmen and Eguinoa, Rubén and Maudrich, Tom and Kenville, Rouven and Irastorza-Landa, Nerea and San Martín, Ricardo and Nikulin, Vadim},
title = {{Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions}},
journal = {Scientific reports},
year = {2026},
month = may,
volume = {16},
number = {1},
pages = {15182},
publisher = {Nature Publishing Group},
issn = {2045-2322},
doi = {10.1038/s41598-026-49471-6},
url = {https://doi.org/10.1038/s41598-026-49471-6},
pmid = {42140985},
pmcid = {PMC13179363}
}

RIS

TY - JOUR
AU - Vidaurre, Carmen
AU - Eguinoa, Rubén
AU - Maudrich, Tom
AU - Kenville, Rouven
AU - Irastorza-Landa, Nerea
AU - San Martín, Ricardo
AU - Nikulin, Vadim
TI - Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions
T2 - Scientific reports
J2 - Sci Rep
PY - 2026
DA - 2026/05/15
VL - 16
IS - 1
SP - 15182
SN - 2045-2322
PB - Nature Publishing Group
DO - 10.1038/s41598-026-49471-6
UR - https://doi.org/10.1038/s41598-026-49471-6
LA - en
ER -

CSL-JSON

{
"id": "10.1038/s41598-026-49471-6",
"type": "article-journal",
"title": "Canonical coherence for the estimation of within- and cross-frequency cortico-kinematic interactions",
"container-title": "Scientific reports",
"author": [
{
"family": "Vidaurre",
"given": "Carmen"
},
{
"family": "Eguinoa",
"given": "Rubén"
},
{
"family": "Maudrich",
"given": "Tom"
},
{
"family": "Kenville",
"given": "Rouven"
},
{
"family": "Irastorza-Landa",
"given": "Nerea"
},
{
"family": "San Martín",
"given": "Ricardo"
},
{
"family": "Nikulin",
"given": "Vadim"
}
],
"container-title-short": "Sci Rep",
"volume": "16",
"issue": "1",
"page": "15182",
"DOI": "10.1038/s41598-026-49471-6",
"PMID": "42140985",
"PMCID": "PMC13179363",
"ISSN": "2045-2322",
"publisher": "Nature Publishing Group",
"URL": "https://doi.org/10.1038/s41598-026-49471-6",
"language": "en",
"issued": {
"date-parts": [
[
2026,
5,
15
]
]
}
}

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

Similar papers

The papers with a page that share the most with this one: the tools found in their code, their categories, datasets, cited references and authors, the rarest counting most.

[1] doi:10.1371/journal.pone.0353371 [code]
Inter-brain functional connectivity: Are we measuring the right thing?
Journal: PloS one
In common: EEG, 3 references
[2] doi:10.1038/s42003-026-10164-5 [code]
The influence of nonlinear resonance on human cortical oscillations.
Journal: Communications biology
In common: Signal Processing Toolbox, EEG, 2 references
[3] doi:10.1111/ejn.70543 [code]
Neural Oscillations Track Subjective and Pupillary Arousal During Naturalistic Movie Viewing.
Journal: The European journal of neuroscience
In common: Signal Processing Toolbox, EEG, 2 references
[4] doi:10.1038/s41467-026-75134-1 [code]
Body surface potential mapping of the cortico-muscular axis using smart textile electrode arrays.
Journal: Nature communications
In common: other, 2 references
[5] doi:10.1111/ejn.70428
Modulation of Corticomuscular Coupling With Split-Belt Locomotor Adaptation in Healthy Young Males.
Journal: The European journal of neuroscience
In common: other, EEG, 2 references
[6] doi:10.1523/eneuro.0346-25.2026 [code]
Effects of TMS on the Decoding and Electrophysiology of Priority in Working Memory.
Journal: eNeuro
In common: Signal Processing Toolbox, other, EEG, 1 reference
[7] doi:10.1038/s41597-026-07146-x [code]
Intention-Action Conflict EEG-Hand Kinematics Dataset for Unimanual Control under Congruent and Incongruent Conditions.
Journal: Scientific data
In common: Signal Processing Toolbox, other, EEG, 1 reference
[8] doi:10.1038/s41597-026-07215-1 [code]
The Brain, Body, and Behavior Dataset (BBBD): Multimodal Recordings during Educational Videos.
Journal: Scientific data
In common: Signal Processing Toolbox, other, EEG, 1 reference
[9] doi:10.1111/psyp.70271 [code]
Disentangling Respiratory Phase-Dependent and Phase-Independent Components of Anticipatory Cardiac Deceleration.
Journal: Psychophysiology
In common: Signal Processing Toolbox, other, EEG, 1 reference
[10] doi:10.1371/journal.pcbi.1014112 [code]
Opposing cortical forces: Alpha slowing and sensorimotor mu acceleration during motor-related BCI training.
Journal: PLoS computational biology
In common: EEG, 2 references

Contribute

The authors of this paper can claim it, correct its record and validate its tracing map, and the maintainers of its code (its owner, or a public member of its organization) correct what it says of their repository; anyone signed in can ask for its removal. Every request goes to OSCR's own machine, which answers it; your account page follows them.

Sign in with ORCID to claim this paper as one of its authors, correct its record or validate its tracing map: when the paper's metadata lists your ORCID iD, you are recognized at once. Maintainers of its code: sign in with GitHub, then claim the repository on your account page.

Request its removal

To ask OSCR to remove this record, the copies of its authors' scripts or its tracing map, use the removal request page: signed in, you say who you are, what to remove and why, then review and confirm the request. Published rules decide every request (how).

Discussion, reproductions, activity

Discussion: questions and error reports about this paper and its code, from signed-in readers and its authors. It opens with sign-in.

Reproductions: reports from readers who ran the authors' code: what they reproduced, with which environment, commit and data. It opens with sign-in.

Activity: what happens around this paper: new versions of its record, its map's validation, discussions and reproductions. It opens with sign-in.