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A new EEG connectivity measure finds amplitude-envelope coupling that phase methods miss, consistently in motor imagery.

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2026-07-13 06:14 UTC pith:YKTYD5MP

load-bearing objection Clean multichannel scattering extension that recovers amplitude-envelope coupling with a real PLI/wPLI dissociation; residual volume conduction after Laplacian still undercuts how strongly we can call that signal "genuine inter-regional." the 4 major comments →

arxiv 2607.08855 v1 pith:YKTYD5MP submitted 2026-07-09 q-bio.NC eess.SPstat.AP

Spatial Neighboring Scattering Transform: A Cross-Channel Amplitude Coupling Measure for EEG Connectivity

Md. Taksimul Ahsan Tawhid , Nasif Ahmed Rafe , Alif Tahmid Priyom , K. M. Mustafizur Rahman This is my paper
classification q-bio.NC eess.SPstat.AP
keywords Spatial Neighboring Scattering Transformwavelet scattering transformamplitude-envelope couplingEEG functional connectivitycross-frequency couplingmotor imageryphase lag index
verification ladder T0 review T1 audit T2 compute T3 formal T4 reserved

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

Phase-based EEG connectivity measures discard amplitude information by design and can miss genuine inter-regional dependence expressed only through co-modulating envelopes. This paper introduces the Spatial Neighboring Scattering Transform (SNST), which extends the wavelet scattering transform to pairs of channels so that first-order coefficients capture amplitude-envelope coupling and second-order coefficients capture how that coupling is itself modulated by slower rhythms. On a public motor-imagery dataset, after Surface Laplacian filtering and a bias-corrected FDR pipeline, the first-order descriptor recovers statistically significant coupling concentrated in a central-parietal electrode neighborhood that is reproduced across all subjects and both left- and right-hand conditions. The second-order descriptor shows this coupling is gated by slow rhythms below about 11 Hz. Under the same statistical procedure, phase lag index and weighted phase lag index recover almost no significant pairs and share zero overlap with SNST, supporting the claim that amplitude-envelope coupling is a largely distinct connectivity signal. A sympathetic reader cares because many clinical and BCI analyses currently ignore this signal by construction.

Core claim

SNST's first-order descriptor identifies statistically significant amplitude-envelope coupling within a central-parietal electrode neighborhood that is spatially consistent across all subjects and both motor-imagery conditions; under an identical bias-corrected FDR pipeline, PLI and wPLI recover negligible significant coupling with zero overlap, so amplitude-envelope coupling constitutes a largely distinct connectivity signal from phase synchronization.

What carries the argument

Spatial Neighboring Scattering Transform (SNST): replace the single-channel modulus of the wavelet scattering transform with a cross-channel conjugate product of band-pass filtered signals, then low-pass average and normalize, yielding first-order envelope-coupling coefficients and second-order coefficients that describe slow modulation of that coupling.

Load-bearing premise

That spatial consistency of FDR-significant electrode pairs across subjects, after Surface Laplacian filtering, is enough to treat the coupling as genuine inter-regional amplitude dependence rather than residual volume conduction or shared noise on a single 22-channel dataset.

What would settle it

Recompute SNST first-order coefficients on the same epochs after source reconstruction or denser high-density EEG with stricter spatial filtering; if the central-parietal significant neighborhood disappears or collapses into volume-conduction patterns also recovered by PLI/wPLI, the claim of a distinct amplitude-domain connectivity signal fails.

Watch this falsifier — get emailed when new claim-graph text bears on it.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit.

Referee Report

4 major / 6 minor

Summary. The manuscript introduces the Spatial Neighboring Scattering Transform (SNST), a multichannel extension of the wavelet scattering transform that replaces the single-channel modulus with a cross-channel conjugate product. This yields two descriptors: S_norm1, quantifying same-scale amplitude-envelope co-modulation between electrode pairs, and S_norm2, quantifying slower-scale modulation of that coupling. On BCI Competition IV-2a (n=9), after Surface Laplacian preprocessing and a bias-corrected one-sample t-test with Benjamini–Hochberg FDR, S_norm1 identifies spatially consistent central-parietal coupling (notably C4–CP4 and neighbors) across all subjects and both left- and right-hand imagery; S_norm2 indicates gating by slow rhythms below ~11 Hz. Under an identical correction pipeline, PLI and wPLI recover at most three significant combinations with zero overlap with SNST, which the authors interpret as evidence that amplitude-envelope coupling is a largely distinct connectivity signal inaccessible to phase-lag measures.

Significance. If the residual-artifact alternative can be ruled out and the method is shown to add information beyond standard amplitude-envelope correlation, SNST would be a useful, deformation-stable descriptor for amplitude-domain and cross-frequency EEG connectivity, with clear equations, synthetic null/planted checks, and matched FDR comparison to PLI/wPLI. The second-order descriptor (modulation of inter-channel coupling strength) is conceptually distinct from classical phase–amplitude CFC and is the more novel contribution. Explicit formulae (Eqs. 2–6), volume-conduction checks for PLV/PLI/wPLI, and an honest limitations section are strengths. The work is currently a single-dataset, sensor-level proof of concept rather than a fully established connectivity standard.

major comments (4)
  1. §3.1–§3.4 and §4: The load-bearing claim that SNST recovers a ‘largely distinct’ genuine inter-regional connectivity signal rests on zero overlap with PLI/wPLI under matched FDR. S_norm1 (Eqs. 2–4) is the time-averaged product of same-scale analytic envelopes; residual common-source or shared-noise components that survive the Laplacian will raise envelope co-fluctuation without producing consistent non-zero phase lag. Post-Laplacian mean pairwise correlation remains 0.249–0.296 (§3.1), and the paper itself notes residual spatial dependence may inflate independent findings (§4). PLI/wPLI are constructed to discard exactly that component, so zero overlap is expected even if a non-trivial fraction of S_norm1 is residual mixing. Spatial consistency across subjects does not break this alternative (same montage/mixing geometry for all subjects). The synthetic checks in §2.4 use independent noi
  2. §2.5 and §3.4 / Table 1: The only external benchmarks are phase-based (PLV, PLI, wPLI). For a paper whose central product is amplitude-envelope coupling, the natural comparators are established amplitude measures—amplitude envelope correlation (AEC) and orthogonalized AEC—not only phase-lag indices. S_norm1 is closely related to scale-wise envelope co-fluctuation; without a head-to-head comparison (same epochs, same FDR pipeline, same seeds), it is unclear whether SNST recovers structure beyond standard AEC or mainly re-expresses it in a scattering framework. The novelty claim for first-order SNST and the interpretation of zero phase-overlap as a new connectivity domain both depend on this missing comparison.
  3. §2.3 Eqs. (5)–(6) and §3.3: S_norm2’s physiological interpretation as ‘slow-rhythm gating of cross-channel coupling’ is interesting but rests on an ad-hoc normalization (division by max(0.1·median S1, ε)) and a paper-defined ‘breadth-of-modulation’ criterion. The Discussion links the <11 Hz range to slow cortical potentials / Bereitschaftspotential without simultaneous SCP recording. Either strengthen the claim with a direct comparison to a standard cross-frequency amplitude–amplitude coupling metric on the same data, or soften the gating language to a descriptive report of second-order coefficient structure and treat the SCP link as a hypothesis for future work.
  4. Validation design (§2.4, Results §3.2): Primary validation is spatial consistency of FDR-significant pairs across n=9 subjects on a single 22-channel public dataset. That is a reasonable exploratory criterion but is soft relative to the abstract/conclusion language that SNST ‘establishes’ a systematically recoverable connectivity domain ‘applicable to any multichannel EEG analysis.’ At minimum, the claims should be scoped to this dataset and montage, and either a second dataset or a clearer leave-one-subject-out / split-session consistency analysis should be added so that the central-parietal pattern is not solely group-averaged on the same nine subjects used for discovery.
minor comments (6)
  1. Figure 6 caption begins with ‘eed-based’ (missing ‘S’); fix typography.
  2. Figure 2 caption: ‘same timed epoch’ → ‘same timed epoch’ / ‘same time epoch’ wording is unclear; clarify that pairs are formed within the same epoch across channels.
  3. §2.3: State explicitly that |(z_m)(z_n)*| = |z_m||z_n| so readers immediately see U1 as an envelope product, not a phase-sensitive cross-spectrum term.
  4. Free parameters (J1,Q1,J2,Q2, Laplacian m/λ, S_norm2 floor 0.1) are listed but sensitivity is not reported; a brief supplementary sweep or justification that results are stable under modest changes would help.
  5. Abstract and Conclusion slightly over-claim relative to the single-dataset offline analysis; align wording with the limitations already stated in §4 (online classification and multi-dataset generalization left for future work).
  6. Reference list and in-text citations are generally appropriate; consider citing orthogonalized AEC / Hipp-style amplitude-correlation connectivity more prominently when framing the amplitude-domain gap.

Circularity Check

0 steps flagged

No circularity: SNST descriptors, significance tests, and PLI/wPLI comparison are independently defined; spatial-consistency validation is a soft criterion that could have failed.

full rationale

The paper's load-bearing chain does not reduce any reported result to its own inputs by construction. S_norm1 and S_norm2 are defined from the multichannel scattering construction (Eqs. 2–6) without reference to motor-imagery labels, electrode neighborhoods, or the eventual findings. Significance is assessed by a one-sample t-test against a cross-pair baseline with Benjamini–Hochberg FDR, not by fitting a target coupling pattern. Synthetic independent-noise and planted-coupling checks are described as external controls run before real-data coefficients. The spatial-consistency criterion (same neighboring electrodes surviving FDR for the same seed across the majority of subjects) is a paper-chosen validation rule, but it does not force S_norm1 values: the statistic could have been non-significant or spatially scattered. The zero-overlap dissociation with PLI/wPLI follows from applying an identical bias-corrected FDR pipeline to independently defined phase measures, not from a self-referential definition. There are no load-bearing self-citations, no uniqueness theorems imported from the authors, no fitted parameters renamed as predictions, and no ansatz smuggled in via prior work by the same group. Residual volume-conduction concerns after the Surface Laplacian are a validity/correctness issue, not circularity. The derivation is self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

5 free parameters · 5 axioms · 2 invented entities

Central claim rests on standard scattering and EEG preprocessing machinery plus a small set of paper-specific operator choices and statistical validation rules. Free parameters are the usual filter-bank and Laplacian knobs plus an ad-hoc floor in second-order normalization. Invented entities are the SNST operator and its two normalized descriptors; independent evidence is the synthetic recovery tests and the public-dataset spatial pattern, not an external physiological assay.

free parameters (5)
  • First-order wavelet bank (J1=6, Q1=2)
    Chosen to cover delta–beta with two filters per octave; not fitted to connectivity outcomes but still a free design choice that defines the frequency grid of all S1 results.
  • Second-order wavelet bank (J2=6, Q2=1)
    Coarser bank for modulation frequencies; design choice that determines which slow rhythms can appear in Snorm2.
  • Snorm2 denominator floor (0.1 · median S1, ε)
    Ad-hoc numerical floor introduced because S1 has no Cauchy–Schwarz ceiling; directly affects magnitude and significance of second-order scores.
  • Spherical-spline Laplacian (m=4, λ=10⁻⁵, 7-term Legendre)
    Standard but free spline parameters; adoption conditioned on reducing mean pairwise correlation in ≥70% of subjects (here all 9).
  • Band-pass 0.5–45 Hz and selective 50 Hz notch
    Preprocessing cutoffs that define the input spectrum to all subsequent coupling estimates.
axioms (5)
  • domain assumption Cross-channel envelope co-modulation (product of analytic wavelet coefficients) is a valid functional-connectivity quantity distinct from phase synchrony.
    Invoked throughout §2.3 and Discussion via citations to Hipp/Engel/Siems; not proved here.
  • domain assumption Surface Laplacian sufficiently suppresses volume-conduction bias for amplitude-envelope measures so remaining significant pairs can be interpreted as inter-regional.
    §2.2 and Results; paper itself notes residual correlation remains (§4).
  • ad hoc to paper Spatial consistency of FDR-significant pairs across subjects and conditions is the primary validation criterion for true coupling.
    Explicitly defined as the validation criterion in Abstract and §2.4; not a standard external benchmark.
  • standard math Morlet wavelets and constant-Q scattering banks are appropriate for EEG envelope analysis.
    Standard scattering construction (Mallat/Andén/Kymatio) adopted in §2.3.
  • domain assumption One-sample t-test across n=9 subjects with BH-FDR is adequate for dense pair×frequency testing.
    §2.4; justified by Wilcoxon power failure at this n, but small-n parametric assumption remains.
invented entities (2)
  • Spatial Neighboring Scattering Transform (SNST) no independent evidence
    purpose: Multichannel extension of WST that replaces single-channel modulus with cross-channel conjugate product to encode amplitude-envelope coupling.
    Core methodological invention; defined by Eqs. (2)–(6).
  • Snorm1 / Snorm2 descriptors no independent evidence
    purpose: Normalized first- and second-order coefficients quantifying envelope co-modulation and its slow-frequency gating.
    The two reported connectivity features; independent handle is only the synthetic recovery and the single-dataset topography.

pith-pipeline@v1.1.0-grok45 · 18761 in / 3721 out tokens · 44587 ms · 2026-07-13T06:14:22.471716+00:00 · methodology

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The functional organization of the brain relies on coordinated activity across spatially distributed regions, making the analysis of inter-regional dependencies fundamental. Existing connectivity measures address this predominantly through phase synchronization, which is vulnerable to volume conduction artifacts and discards amplitude-domain coupling. This study introduces the Spatial Neighboring Scattering Transform, which extends the wavelet scattering transform to the multichannel setting, yielding two descriptors that jointly capture amplitude-envelope coupling between channels and its modulation across frequency scales. SNST was evaluated on the BCI Competition IV-2a motor imagery dataset using a bias-corrected, false-discovery-rate-controlled statistical pipeline, with the validation criterion defined as spatial consistency of significant coupling across subjects. The first-order descriptor identified statistically significant amplitude coupling within a central-parietal electrode neighborhood, reproduced consistently across all subjects and both imagery conditions. The second-order descriptor revealed that this coupling is periodically gated by slow rhythms, indicating a cross-frequency amplitude-modulation structure absent from single-frequency connectivity measures. Phase lag index and weighted phase lag index, computed under an identical correction procedure and verified robust to volume conduction, identified negligible significant coupling with zero overlap with SNST findings, demonstrating that amplitude envelope coupling constitutes a largely distinct connectivity signal. These results establish SNST as a cross-channel scattering-based connectivity descriptor that recovers amplitude-envelope and cross-frequency coupling structure systematically, applicable to any multichannel EEG analysis where amplitude-domain inter-regional dependence is of interest.

Figures

Figures reproduced from arXiv: 2607.08855 by Alif Tahmid Priyom, K. M. Mustafizur Rahman, Md. Taksimul Ahsan Tawhid, Nasif Ahmed Rafe.

Figure 1
Figure 1. Figure 1: Methodological flowchart of the overall EEG processing and analytical pipeline where 𝜓𝜆 is a band-pass wavelet centered at frequency 𝜆, 𝜙𝐽 is a low-pass averaging window with invariance scale 𝑇 = 2𝐽 samples, and the outer parentheses indicate that the entire convolution chain, not 𝜙𝐽 alone, is evaluated at time 𝑡. SNST generalizes this construction to the multichannel setting by replacing the single-channe… view at source ↗
Figure 2
Figure 2. Figure 2: Schematic representation of multilevel coefficient extraction using the proposed Spatial Neighboring Scattering Transform (SNST). For the first epoch of channel-1, the coefficient will be extracted from 2nd,3rd,...upto channel-k with the same timed epoch. within the reliable passband, covering the full delta-through￾beta EEG spectrum with two filters per octave. The second￾order bank used 𝐽2 = 6 and 𝑄2 = 1… view at source ↗
Figure 3
Figure 3. Figure 3: Comparison of raw and filtered EEG signals for [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figure 4
Figure 4. Figure 4: Impact of the Surface Laplacian transform on EEG spatial resolution and cross-channel connectivity 3.3. 𝑆 norm 2 Identifies Slow-Rhythm Gating of Cross-Frequency Envelope Coupling Applying the breadth-of-modulation criterion to 𝑆 norm 2 — the proportion of candidate fast-carrier frequencies showing elevated coupling for a given slow frequency identified 396 of 1,386 tested (pair, slow-frequency) combinatio… view at source ↗
Figure 5
Figure 5. Figure 5: Topographic visualization of amplitude envelope modulation and neighboring channel influence for C3 and C4 seed configurations during left- and right-hand motor imagery. that the near-total absence of phase-based significant cou￾pling found here reflects a genuine methodological distinc￾tion rather than an absence of inter-regional structure in the data. To compare 𝑆 norm 1 directly against PLI and wPLI on… view at source ↗
Figure 6
Figure 6. Figure 6: eed-based scalp topographies of the breadth-of-modulation fraction (𝑆 norm 2 ) under left- and right-hand motor imagery conditions. Panels demonstrate spatial co-localization of slow-rhythm gating patterns within localized centro-parietal neighborhoods for both C4 and C3 seed configurations. 4. Discussion This study introduced SNST to address a gap recog￾nized across the connectivity literature: phase-base… view at source ↗
Figure 7
Figure 7. Figure 7: Histograms of raw 𝑝-value distributions from one-sample 𝑡-tests (prior to FDR correction) comparing the proposed SNST 𝑆 norm 1 , PLI, and wPLI metrics [PITH_FULL_IMAGE:figures/full_fig_p009_7.png] view at source ↗

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Reference graph

Works this paper leans on

43 extracted references · 25 canonical work pages · 1 internal anchor

  1. [1]

    Functional and Effective Connectiv- ity: A Review

    Friston K. Functional and Effective Connectiv- ity: A Review. Brain Connectivity 2011;1:13–36. https://doi.org/10.1089/brain.2011.0008

    doi:10.1089/brain.2011.0008 2011

  2. [2]

    Large-scale brain networks in cognition: emerging methods and principles

    Bressler SL, Menon V. Large-scale brain networks in cognition: emerging methods and principles. Trends in Cognitive Sciences 2010;14:277–90. https://doi.org/10.1016/j.tics.2010.04.004

    doi:10.1016/j.tics.2010.04.004 2010

  3. [3]

    Complex brain networks: graph theoretical analysisof structuraland functionalsystems

    Bullmore ET, Sporns O. Complex brain networks: graph theoretical analysisof structuraland functionalsystems. NatureReviews Neuro- science 2009;10:186–98. https://doi.org/10.1038/nrn2575. M.T.A. Tawhid et al.:Preprint submitted to ElsevierPage 10 of 12 Spatial Neighboring Scattering Transform

    doi:10.1038/nrn2575 2009

  4. [4]

    Modern network science of neurological disorders

    Stam CJ. Modern network science of neurological disorders. Nature Reviews Neuroscience 2014;15:683–95. https://doi.org/10.1038/nrn3801

    work page doi:10.1038/nrn3801 2014

  5. [5]

    Electroencephalography source connectivity: toward high time/space resolution brain networks

    HassanM,WendlingF.Electroencephalographysourceconnectivity: toward high time/space resolution brain networks. arXiv (Cornell University) 2018. https://doi.org/10.48550/arxiv.1801.02549

    work page internal anchor Pith review Pith/arXiv arXiv doi:10.48550/arxiv.1801.02549 2018

  6. [6]

    Complex network measures of brain con- nectivity: Uses and interpretations

    Rubinov M, Sporns O. Complex network measures of brain con- nectivity: Uses and interpretations. NeuroImage 2009;52:1059–69. https://doi.org/10.1016/j.neuroimage.2009.10.003

    doi:10.1016/j.neuroimage.2009.10.003 2009

  7. [7]

    Graph theoretical analysis of magnetoencephalographicfunctionalconnectivityinAlzheimer’sdis- ease

    Stam CJ, Haan W de, Daffertshofer A, Jones BF, Manshanden I, Walsum AM van C van, Montez T, Verbunt JPA, Munck JC de, Dijk BW van, Berendse HW, Scheltens P. Graph theoretical analysis of magnetoencephalographicfunctionalconnectivityinAlzheimer’sdis- ease. Brain 2008;132:213–24. https://doi.org/10.1093/brain/awn262

    work page doi:10.1093/brain/awn262 2008

  8. [8]

    Using partial directed coherence to de- scribeneuronalensembleinteractions.JournalofNeuroscienceMeth- ods 1999;94:93–103

    Sameshima K, Baccalá LA. Using partial directed coherence to de- scribeneuronalensembleinteractions.JournalofNeuroscienceMeth- ods 1999;94:93–103. https://doi.org/10.1016/s0165-0270(99)00128- 4

    work page doi:10.1016/s0165-0270(99)00128- 1999

  9. [9]

    Measuring phase synchrony in brain signals

    Lachaux J-P, Rodríguez E, Martinerie J, Varela FJ. Measuring phase synchrony in brain signals. Human Brain Mapping 1999;8:194–208. https://doi.org/10.1002/(sici)1097-0193(1999)8:4<194::aid- hbm4>3.0.co;2-c

    doi:10.1002/(sici)1097-0193(1999)8:4 1999

  10. [10]

    High Gamma Power Is Phase-Locked to Theta Oscillations in Human Neocortex

    Canolty RT, Edwards E, Dalal SS, Soltani M, Nagarajan S, Kirsch HE, Berger MS, Barbaro N, Knight RT. High Gamma Power Is Phase-Locked to Theta Oscillations in Human Neocortex. Science 2006;313:1626–8. https://doi.org/10.1126/science.1128115

    work page doi:10.1126/science.1128115 2006

  11. [11]

    Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources

    Stam CJ, Nolte G, Daffertshofer A. Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources. Human Brain Mapping 2007;28:1178–93. https://doi.org/10.1002/hbm.20346

    work page doi:10.1002/hbm.20346 2007

  12. [12]

    An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias

    Vinck M, Oostenveld R, Wingerden M van, Battaglia FP, Pennartz CMA. An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias. NeuroImage 2011;55:1548–65. https://doi.org/10.1016/j.neuroimage.2011.01.055

    work page doi:10.1016/j.neuroimage.2011.01.055 2011

  13. [13]

    Group Invariant Scattering

    Mallat S. Group Invariant Scattering. Communications on Pure and Applied Mathematics 2012;65:1331–98. https://doi.org/10.1002/cpa.21413

    doi:10.1002/cpa.21413 2012

  14. [14]

    https://doi.org/10.1109/tsp.2014.2326991

    AndénJ,MallatS.DeepScatteringSpectrum.arXiv(CornellUniver- sity) 2014;62:4114–28. https://doi.org/10.1109/tsp.2014.2326991

    doi:10.1109/tsp.2014.2326991 2014

  15. [15]

    Classification of alcoholic EEG signals using wavelet scattering transform-based features

    Buriro AB, Ahmed B, Baloch G, Ahmed J, Shoorangiz R, Weddell SJ, Jones RD. Classification of alcoholic EEG signals using wavelet scattering transform-based features. Computers in Biology and Medicine 2021;139:104969–104969. https://doi.org/10.1016/j.compbiomed.2021.104969

    doi:10.1016/j.compbiomed.2021.104969 2021

  16. [16]

    Wavelet transforms for feature engineering in EEG data processing: An application on Schizophrenia

    Gosala B, Kapgate PD, Jain P, Chaurasia RN, Gupta M. Wavelet transforms for feature engineering in EEG data processing: An application on Schizophrenia. Biomedical Signal Processing and Control 2023;85:104811–104811. https://doi.org/10.1016/j.bspc.2023.104811

    doi:10.1016/j.bspc.2023.104811 2023

  17. [17]

    Comparison Analysis: Granger Causality and New Causality and Their Applications to Motor Imagery

    Hu S, Wang H, Zhang J, Kong W, Cao Y, Kozma R. Comparison Analysis: Granger Causality and New Causality and Their Applications to Motor Imagery. IEEE Transactions on Neural Networks and Learning Systems 2015;27:1429–44. https://doi.org/10.1109/tnnls.2015.2441137

    work page doi:10.1109/tnnls.2015.2441137 2015

  18. [18]

    https://doi.org/10.3389/fnins.2012.00055

    Tangermann M, Müller K, Aertsen A, Birbaumer N, Braun C, Brun- ner C, Leeb R, Mehring C, Miller KJ, Müller-Putz G, Nolte G, Pfurtscheller G, Preißl H, Schalk G, Schlögl A, Vidaurre C, Waldert S,BlankertzB.ReviewoftheBCICompetitionIV.FrontiersinNeu- roscience 2012;6:55–55. https://doi.org/10.3389/fnins.2012.00055

    Pith/arXiv arXiv doi:10.3389/fnins.2012.00055 2012

  19. [19]

    Digital filter design for electrophysiological data – a practical approach

    Widmann A, Schröger E, Maeß B. Digital filter design for electrophysiological data – a practical approach. Journal of Neuroscience Methods 2014;250:34–46. https://doi.org/10.1016/j.jneumeth.2014.08.002

    doi:10.1016/j.jneumeth.2014.08.002 2014

  20. [20]

    A fully automated correction method of EOG arti- factsinEEGrecordings.ClinicalNeurophysiology2006;118:98–104

    Schlögl A, Keinrath C, Zimmermann D, Scherer R, Leeb R, Pfurtscheller G. A fully automated correction method of EOG arti- factsinEEGrecordings.ClinicalNeurophysiology2006;118:98–104. https://doi.org/10.1016/j.clinph.2006.09.003

    work page doi:10.1016/j.clinph.2006.09.003 2006

  21. [21]

    Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial re- view

    Kayser J, Tenke CE. Issues and considerations for using the scalp surface Laplacian in EEG/ERP research: A tutorial re- view. International Journal of Psychophysiology 2015;97:189–209. https://doi.org/10.1016/j.ijpsycho.2015.04.012

    work page doi:10.1016/j.ijpsycho.2015.04.012 2015

  22. [22]

    Current Source Den- sity Estimation Enhances the Performance of Motor-Imagery- Related Brain–Computer Interface

    Rathee D, Raza H, Prasad G, Cecotti H. Current Source Den- sity Estimation Enhances the Performance of Motor-Imagery- Related Brain–Computer Interface. IEEE Transactions on Neu- ral Systems and Rehabilitation Engineering 2017;25:2461–71. https://doi.org/10.1109/tnsre.2017.2726779

    work page doi:10.1109/tnsre.2017.2726779 2017

  23. [23]

    Electric Fields of the Brain

    Nunez PL, Srinivasan RC. Electric Fields of the Brain. Oxford University Press; 2006. https://doi.org/10.1093/acprof:oso/9780195050387.001.0001

    doi:10.1093/acprof:oso/9780195050387.001.0001 2006

  24. [24]

    Spherical splines for scalp potential and current density mapping

    Perrin F, Pernier J, Bertrand O, Echallier JF. Spherical splines for scalp potential and current density mapping. Electroencephalography and Clinical Neurophysiology 1989;72:184–7. https://doi.org/10.1016/0013-4694(89)90180-6

    doi:10.1016/0013-4694(89)90180-6 1989

  25. [25]

    Invariant Scattering Convolution Networks

    [25] Bruna J, Mallat S. Invariant Scattering Convolution Networks. IEEE Transactions on Pattern Analysis and Machine Intelligence 2013;35:1872–86. https://doi.org/10.1109/tpami.2012.230

    doi:10.1109/tpami.2012.230 2013

  26. [26]

    Dissociated neuronal phase- and amplitude-coupling patterns in the human brain

    Siems M, Siegel M. Dissociated neuronal phase- and amplitude-coupling patterns in the human brain. NeuroImage 2020;209:116538–116538. https://doi.org/10.1016/j.neuroimage.2020.116538

    work page doi:10.1016/j.neuroimage.2020.116538 2020

  27. [27]

    Sensitivity of amplitude and phase based MEG measures of interhemispheric connectivity during unilateralfingermovements.NeuroImage2021;242:118457–118457

    WeiHT,Francois-NienaberA,DeschampsT,BellanaB,HebscherM, Sivaratnam G, zadeh MM, Meltzer JA. Sensitivity of amplitude and phase based MEG measures of interhemispheric connectivity during unilateralfingermovements.NeuroImage2021;242:118457–118457. https://doi.org/10.1016/j.neuroimage.2021.118457

    work page doi:10.1016/j.neuroimage.2021.118457 2021

  28. [28]

    Kymatio: Scattering Transforms in Python

    Andreux M, Angles T, Exarchakis G, Leonarduzzi R, Rochette G, ThiryL,ZarkaJ,MallatS,AndénJ,BelilovskyE,BrunaJ,Lostanlen V, Chaudhary M, Hirn M, Oyallon E, Zhang S, Cella C-E, Eicken- berg M. Kymatio: Scattering Transforms in Python. arXiv (Cornell University) 2018. https://doi.org/10.48550/arxiv.1812.11214

    Pith/arXiv arXiv doi:10.48550/arxiv.1812.11214 2018

  29. [29]

    Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing

    Benjamini Y, Hochberg Y. Controlling the False Discovery Rate: A Practical and Powerful Approach to Multiple Testing. Journal of the Royal Statistical Society Series B (Statistical Methodology) 1995;57:289–300. https://doi.org/10.1111/j.2517- 6161.1995.tb02031.x

    doi:10.1111/j.2517- 1995

  30. [30]

    The 10-20 Electrode System and Cerebral Lo- cation

    Homan RW. The 10-20 Electrode System and Cerebral Lo- cation. American Journal of EEG Technology 1988;28:269–79. https://doi.org/10.1080/00029238.1988.11080272

    doi:10.1080/00029238.1988.11080272 1988

  31. [31]

    MEG and EEG data analysis with MNE- Python

    Gramfort A. MEG and EEG data analysis with MNE- Python. Frontiers in Neuroscience 2013;7:267–267. https://doi.org/10.3389/fnins.2013.00267

    doi:10.3389/fnins.2013.00267 2013

  32. [32]

    Spatial filtering and neocortical dynamics: estimates of EEG coherence

    Srinivasan R, Nunez PL, Silberstein RB. Spatial filtering and neocortical dynamics: estimates of EEG coherence. IEEE Transactions on Biomedical Engineering 1998;45:814–26. https://doi.org/10.1109/10.686789

    work page doi:10.1109/10.686789 1998

  33. [33]

    EEG coherency

    Nunez PL, Srinivasan R, Westdorp AF, Wijesinghe RS, Tucker DM, Silberstein RB, Cadusch PJ. EEG coherency. I: Statistics, reference electrode, volume conduction, Laplacians, cortical imaging, and in- terpretation at multiple scales. Electroencephalography and Clinical Neurophysiology 1997;103:499–515. https://doi.org/10.1016/s0013- 4694(97)00066-7

    work page doi:10.1016/s0013- 1997

  34. [34]

    Revealing brain connectivity: graph embeddings for EEG representation learning and comparative analysis of structural and functional connectivity

    Almohammadi A, Wang Y. Revealing brain connectivity: graph embeddings for EEG representation learning and comparative analysis of structural and functional connectivity. Frontiers in Neuroscience 2024;17:1288433–1288433. https://doi.org/10.3389/fnins.2023.1288433

    work page doi:10.3389/fnins.2023.1288433 2024

  35. [35]

    Coherence based graph convolution network for motor imagery-induced EEG after spinal cord injury

    Li H, Liu M, Yu X, Zhu J, Wang C, Chen X, Feng C, Leng J, Zhang Y, Xu F. Coherence based graph convolution network for motor imagery-induced EEG after spinal cord injury. Frontiers in Neuroscience 2023;16:1097660–1097660. https://doi.org/10.3389/fnins.2022.1097660

    work page doi:10.3389/fnins.2022.1097660 2023

  36. [36]

    Large-scale cortical correlation structure of spontaneous oscillatory activity

    Hipp JF, Hawellek DJ, Corbetta M, Siegel M, Engel AK. Large-scale cortical correlation structure of spontaneous oscillatory activity. Na- ture Neuroscience 2012;15:884–90. https://doi.org/10.1038/nn.3101. M.T.A. Tawhid et al.:Preprint submitted to ElsevierPage 11 of 12 Spatial Neighboring Scattering Transform

    work page doi:10.1038/nn.3101 2012

  37. [37]

    Intrinsic Coupling Modes: Multiscale Interactions in Ongoing Brain Activity

    Engel AK, Gerloff C, Hilgetag CC, Nolte G. Intrinsic Coupling Modes: Multiscale Interactions in Ongoing Brain Activity. Neuron 2013;80:867–86. https://doi.org/10.1016/j.neuron.2013.09.038

    work page doi:10.1016/j.neuron.2013.09.038 2013

  38. [38]

    Resting State EEG Directed Functional Connectivity Unveils Changes in Motor Network Organization in Subacute Stroke Patients After Rehabilitation

    Pirovano I, Mastropietro A, Antonacci Y, Barà C, Guanziroli E, Molteni F, Faes L, Rizzo G. Resting State EEG Directed Functional Connectivity Unveils Changes in Motor Network Organization in Subacute Stroke Patients After Rehabilitation. Frontiers in Physiology 2022;13:862207–862207. https://doi.org/10.3389/fphys.2022.862207

    work page doi:10.3389/fphys.2022.862207 2022

  39. [39]

    Slow po- tentials of the cerebral cortex and behavior

    Birbaumer N, Elbert T, Canavan AGM, Rockstroh B. Slow po- tentials of the cerebral cortex and behavior. Physiological Reviews 1990;70:1–41. https://doi.org/10.1152/physrev.1990.70.1.1

    work page doi:10.1152/physrev.1990.70.1.1 1990

  40. [40]

    Movement re- lated slow cortical potentials in severely paralyzed chronic stroke patients

    Yilmaz Ö, Birbaumer N, Ramos-Murguialday A. Movement re- lated slow cortical potentials in severely paralyzed chronic stroke patients. Frontiers in Human Neuroscience 2015;8:1033–1033. https://doi.org/10.3389/fnhum.2014.01033

    work page doi:10.3389/fnhum.2014.01033 2015

  41. [41]

    Ghost interactions in MEG/EEG source space: A note of caution on inter- areal coupling measures

    Palva JM, Wang SH, Palva S, Zhigalov A, Monto S, Brookes MJ, Schoffelen J, Jerbi K. Ghost interactions in MEG/EEG source space: A note of caution on inter- areal coupling measures. NeuroImage 2018;173:632–43. https://doi.org/10.1016/j.neuroimage.2018.02.032

    work page doi:10.1016/j.neuroimage.2018.02.032 2018

  42. [42]

    Mallat’s Scattering Transform Based Anomaly Sensing for Detection of Seizures in Scalp EEG

    Ahmad MZ, Kamboh AM, Saleem S, Khan A. Mallat’s Scattering Transform Based Anomaly Sensing for Detection of Seizures in Scalp EEG. IEEE Access 2017;5:16919–29. https://doi.org/10.1109/access.2017.2736014

    work page doi:10.1109/access.2017.2736014 2017

  43. [43]

    Benchmarking metrics for inferring functional connectivity from multi-channel EEG and MEG: A simulation study

    Yu M. Benchmarking metrics for inferring functional connectivity from multi-channel EEG and MEG: A simulation study. Chaos An Interdisciplinary Journal of Nonlinear Science 2020;30:123124–123124. https://doi.org/10.1063/5.0018826. M.T.A. Tawhid et al.:Preprint submitted to ElsevierPage 12 of 12

    work page doi:10.1063/5.0018826 2020