{"id":"3dd5e19b-b499-476e-9da3-6982d740c26c","arxiv_id":"2501.07394","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":4,"one_line_summary":"Resting-state EEG connection weights are consistently right-skewed and relatively uniform across electrode montages and connectivity measures.","lead":"Does the strength of connections in resting-state EEG brain networks follow a consistent pattern? This study combines simulations and a large real-world EEG database to show that connection weights are consistently right-skewed and relatively uniform, with volume conduction shaping how average strength links to distribution form.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Entropy values for signed connectivity measures are computed on a stated [0,1] binning; iCOH and AEC are negative-capable, so the uniformity/volume-conduction claim rests on an undocumented transform.","rationale":"The reader identified the same weak point, and I agree it is the most load-bearing issue. The paper's central contribution is not only that weights are right-skewed—that part survives negative values—but that the distribution is relatively uniform and that coupling-measure differences track volume conduction. That second claim is quantified almost entirely by Shannon entropy (Section 2.4.2, Eq. 8; Figs. 5-7). Because the binning is explicitly fixed to [0,1] while iCOH and AEC generate negative weights, the reported SE values are not well-defined without an undocumented preprocessing step. This is an internal inconsistency, not a disagreement with consensus: Eq. (8) as written cannot be applied to a vector containing values outside [0,1] without clipping, shifting, or dropping values, and none of these is described. The normative validation covers only COH and iCOH, so it cannot independently establish the behavior of AEC or PLI; the simulation is the only evidence for those measures, which makes the missing transform more consequential. The secondary missing-repetition issue in Section 2.1.1 reinforces the need for clarification but is not the primary reason for conditional acceptance. I do not consider the findings impossible or the authors dishonest; both gaps are fixable by reanalysis and reporting. The conditional verdict remains appropriate: if the authors supply the transform and recomputed SE values, plus the repetition details, the claims may stand; if not, the uniformity and volume-conduction conclusions should be withdrawn. Since the reader already issued CONDITIONAL, my read does not move the verdict.","tokens_in":13193,"tokens_out":8465,"duration_ms":81796,"concrete_test":"Reconstruct the Section 2.1 simulation (or obtain the authors' code/data) and recompute iCOH and AEC upper-triangle weights exactly as specified. Then calculate SE three ways: (i) bin raw values over [-1,1] with 100 equal bins and normalize by log(100); (ii) min-max rescale the raw vector to [0,1] before the 100-bin histogram; (iii) take absolute values before binning. Compare the resulting SE ranges and MCW-SE correlations with Figs. 5-7. If variants (i) or (ii) put iCOH/AEC in the 0.7-0.9 range or remove the MCW-SE contrast, the uniformity and volume-conduction conclusions collapse; if the reported 0.3-0.55 values appear only after silent truncation, the published numbers are artifacts. Also rerun the full pipeline with at least 100 independent source selections to confirm the invariance claim.","verdict_should_be":"UNCHANGED","load_bearing_attack":"Section 2.4.2 fixes the histogram support to [0,1] (100 bins of width 0.01) and defines Shannon entropy normalized by log N. However, iCOH (Eq. 4, imaginary part of coherency) and AEC (Section 2.3.4, Pearson correlation of amplitude envelopes) have natural support [-1,1] and take negative values. The text never states that absolute values are taken or that weights are rescaled before binning. Unless such a transform is silently applied, negative entries fall outside the bins, so the SE reported in Figs. 5-7 for iCOH and AEC is not the entropy of the full weight distribution and is not comparable to the SE of COH/PLV/PLI. Any silent treatment—clipping, dropping, or absolute value—would change the histogram and would also make the MCW-SE correlation internally inconsistent if MCW is computed on the full upper triangle while SE is computed on a truncated vector. This directly affects the claimed pattern that SE differs across coupling measures and the inference that the effect is related to volume conduction (Results 3.1.3, Discussion). Skewness and kurtosis do not require [0,1] support, so the right-skewness claim is less affected; the load-bearing gap is specifically the uniformity comparison. A secondary reproducibility gap: Section 2.1.1 reports a single random selection of 200 sources, with no stated repetition count, while the scatter/correlation analyses in Figs. 3-5 imply multiple realizations.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper investigates the statistical distribution of connectivity weights in fully connected resting-state EEG networks. Using a forward-model simulation with realistic intracranial EEG sources and four electrode montages (19, 32, 64, 128 channels), the authors construct networks with five coupling measures (COH, iCOH, PLV, PLI, AEC) and quantify the weight distributions via mean, skewness, kurtosis, and Shannon entropy. They report that the weights are right-skewed regardless of channel density or coupling measure, that the distributions are relatively uniform, and that volume conduction affects the degree of uniformity and the correlation between mean connection weight and distribution shape. The simulation findings are then validated in a large normative EEG database using COH and iCOH.","tokens_in":13525,"tokens_out":3368,"duration_ms":32039,"significance":"If the main claims hold, the paper offers a potentially useful empirical regularity: the shape of the functional connectivity weight distribution in resting-state scalp EEG is stable across electrode density and coupling metrics, with a documented role for volume conduction. The strengths of the study include the use of realistic iEEG-derived sources, a forward-modeling pipeline, multiple channel densities and coupling measures, and external validation on a large multicenter normative database. However, the central uniformity comparison currently rests on a questionable computation of Shannon entropy for signed connectivity measures, and the simulation's reproducibility is undermined by an unstated number of realizations. These issues need to be resolved before the conclusions can be accepted.","major_comments":[{"comment":"The simulation description reports a single random selection of 200 iEEG sources with 10,000 samples each, but no repetition count. Figures 3-5 show scatter plots with many points per condition, implying either multiple random source selections, multiple noise draws, or both. As written, the statistical results (Pearson correlations in Figs. 3-5) are not reproducible and the scatter density cannot be assessed. Please state the number of independent realizations and, if only one was used, explain how the scatter points in each subplot were generated.","section":"Section 2.1.1"}],"minor_comments":[{"comment":"The heading states that the network connection weights 'display a leptokurtic distribution,' but the text and Fig. 4 indicate kurtosis consistently less than 3, which is platykurtic. Please correct the heading to match the reported results.","section":"Section 3.1.2"},{"comment":"In the final sentence of this section, the text says there is no correlation between kurtosis and mean connectivity weights for 'iCOH and PLV,' but the preceding sentence refers to COH, PLV, and AEC; the intended contrast is presumably with iCOH and PLI, as shown in Fig. 4. Please correct this inconsistency.","section":"Section 3.1.2"},{"comment":"Equation (8) appears garbled in the manuscript ('2 12 1SE log ( )log N i i i P P N = −= ∑'). Please reformat the equation so that the summation and normalization are clearly displayed.","section":"Section 2.4.2"},{"comment":"The phrase 'volumetric conduction' appears in the paragraph discussing Fig. 6 and Fig. 7; this should read 'volume conduction' for consistency with the rest of the paper.","section":"Discussion"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is within scope for a neuroimaging methods venue, and the main idea is interesting, but the handling of signed connectivity measures in the entropy computation is load-bearing and must be fixed. The missing repetition count in the simulation is also a reproducibility issue that the authors should address. I do not see grounds for rejection, as the problems appear correctable within the manuscript's scope."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Quick take: this is a careful descriptive study with a modest but real new observation—across four channel densities and five coupling measures, resting-state EEG connectivity weights are consistently right-skewed, and the shape does not move much with montage. The validation on 1791 normative recordings is a genuine plus, and the authors are upfront that only COH and iCOH could be tested there.\n\nThe main thing to verify before trusting the uniformity claim: Section 2.4.2 fixes the histogram support at [0,1] for Shannon entropy, but iCOH and AEC can take negative values. The paper never says it takes absolute values or rescales. If negative entries are silently dropped or clipped, the entropy numbers for those measures are not comparable to COH/PLV/PLI, and the volume-conduction interpretation in Figure 5 rests on an artifact. Skewness and kurtosis don't need [0,1], so the right-skewness and platykurtic claims are on firmer ground. The stress-test note is right, and the authors need to state the transform or recompute.\n\nSecond issue: the simulation section mentions one random selection of 200 iEEG sources, but Figures 3-5 show many points per condition. Either multiple realizations happened and weren't reported, or the scatter is across something else. That needs a sentence. Also, no code or parameter list (window sizes, noise amplitudes) is provided, which makes replication harder than it should be for a simulation paper.\n\nMinor: the normative validation covers two of five measures, and the authors admit it. That's a limitation, not a fatal flaw. The within-study logic is otherwise not circular—no parameters are fit to the normative data.\n\nWho's this for: anyone doing thresholding or QC on scalp EEG networks. It's not a breakthrough, but a useful normative baseline if the entropy fix checks out. I'd take it in a reading group, and I'd send it to review—the issues are addressable in revision and the descriptive result is worth having on record. Recommend engage, with the transform question as the main referee ask.","headline":"A solid descriptive study with a real new observation—right-skewed EEG connectivity weights across montages and measures—but the Shannon entropy numbers for signed measures rest on an undocumented transform, and the simulation needs a repetition count.","tokens_in":14064,"tokens_out":1638,"would_cite":true,"duration_ms":16476,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"The paper claims that functional connectivity weights in resting-state EEG networks are right-skewed, platykurtic, and relatively uniform regardless of channel density or coupling measure, with volume conduction explaining which measures…","keywords":["resting-state EEG","functional connectivity","connectivity weight distribution","skewness","kurtosis","Shannon entropy","volume conduction","channel density"],"falsifier":"Recompute skewness, kurtosis, and Shannon entropy for the simulated imaginary-coherence and amplitude-envelope-correlation networks after an explicit nonnegative transformation such as taking absolute values or shifting weights to [0,1]; if the right skew, kurtosis below 3, or entropy ranges change materially, the claimed independence from coupling measure is an artifact of the missing handling step.","tokens_in":12964,"feed_emoji":"🧠","tokens_out":9276,"duration_ms":77443,"temperature":0.7,"pith_summary":"This paper asks whether the raw weights of fully connected resting-state EEG networks follow a stable statistical shape before the usual thresholding step that discards weak links. Using forward simulations of scalp EEG at 19, 32, 64, and 128 channels and five coupling measures, it reports that connection weights are consistently right-skewed, flatter than a normal distribution, and relatively uniform, and that channel density and coupling choice barely change that shape. It then validates the main pattern on a large normative EEG database using coherence and imaginary coherence across frequency bands. If the shape is genuinely stable, descriptors of the weight distribution become a principled baseline for network thresholding, data quality control, and cross-study or clinical comparisons.","feed_headline":"Resting EEG weights stay right-skewed from 19 to 128 channels","feed_subtitle":"Forward simulation and 1,791 recordings show the shape does not depend on montage or coupling measure.","key_machinery":"The argument is carried by three shape descriptors computed on the upper-triangle entries of each symmetric functional-connectivity matrix: skewness (third standardized moment), kurtosis (fourth standardized moment), and Shannon entropy of a 100-bin histogram over the weight range [0,1], normalized so 0 means clustered and 1 means uniform. These descriptors compress an entire network into a few numbers that can be compared across montages and coupling measures. The volume-conduction effect is identified by contrasting measures known to be sensitive to it (coherence, phase-locking value, amplitude envelope correlation) with measures designed to suppress it (imaginary part of coherency, phase-lag index); the stability claim rests on the descriptors staying in the same qualitative range across all combinations.","core_discovery":"The central claim is that the distribution of functional connectivity weights in resting-state scalp EEG is a stable feature: it is right-skewed (positive skewness), platykurtic (kurtosis below 3), and relatively uniform as measured by Shannon entropy, and this shape does not depend on whether the network is built from 19, 32, 64, or 128 channels or from any of five coupling measures (coherence, imaginary part of coherency, phase-locking value, phase-lag index, amplitude envelope correlation). The paper further claims that volume conduction, the passive spread of one brain source across many electrodes, separates the measures: for coherence, phase-locking value, and amplitude envelope correlation the mean connection weight correlates strongly with skewness, kurtosis, and entropy, whereas for the volume-conduction-robust imaginary coherence and phase-lag index these correlations weaken and the entropy is lower. The normative-data validation with coherence and imaginary coherence reproduces the right skew, the negative mean-kurtosis correlation, and the frequency-band pattern, with alpha-band networks showing larger weights and a more uniform distribution.","pith_inferences":["If the right-skewed shape is genuinely invariant, it supplies a null model for anomaly detection: a patient resting-state network whose skewness-entropy relationship departs from the expected curve could be flagged for clinical scrutiny without needing a matched control group.","The paper's own remark that source-level connectivity may be more right-skewed and leptokurtic suggests the scalp-level uniformity is partly a volume-conduction smoothing effect; recomputing the same descriptors on source-reconstructed EEG would separate smoothing from genuine coupling structure.","A direct audit of how negative imaginary-coherence and envelope-correlation values were handled before binning would settle whether the claimed invariance across coupling measures survives an explicit nonnegative transformation.","Applying the same simulation-plus-validation workflow to MEG or fNIRS data would show whether the stable shape is a general electrophysiological property or specific to scalp EEG."],"forward_implications":["Thresholding a resting-state network by keeping only strong links removes the long right tail of a right-skewed weight distribution, so the surviving network is a systematically selected tail rather than a random subsample of connections.","Because the right skew and the mean-entropy correlation persist from 19 to 128 channels, distribution shape can serve as a montage-invariant reference when comparing studies that used different electrode densities.","For volume-conduction-sensitive measures, the mean connection weight carries information about skewness and kurtosis, while for volume-conduction-robust measures it does not, so mean-based shortcuts must be interpreted separately for each measure.","The lower Shannon entropy of imaginary-coherence and phase-lag-index networks implies that volume-conduction-robust measures expose a less uniform weight structure that may reflect true neural coupling more directly."],"supporting_citations":[{"why":"Supplies the multicenter normative EEG cross-spectra used to validate the simulated distribution findings.","marker":"[22]"},{"why":"Supplies the real intracranial EEG signals used as cortical sources in the forward simulation.","marker":"[19]"},{"why":"Provides the boundary-element forward solver used to compute scalp EEG from cortical sources.","marker":"[20]"},{"why":"Provides the head-model and electrode-configuration pipeline for the forward solution.","marker":"[21]"},{"why":"Defines the imaginary part of coherency, one of the five coupling measures.","marker":"[25]"},{"why":"Defines the phase-lag index, the volume-conduction-robust measure contrasted with coherence-based measures.","marker":"[28]"},{"why":"Defines amplitude envelope correlation, one of the volume-conduction-sensitive coupling measures.","marker":"[29]"},{"why":"Supplies the mathematical relations between coupling measures that restrict normative validation to coherence and imaginary coherence.","marker":"[27]"},{"why":"Introduces Shannon entropy as the uniformity measure for network connection weight distributions.","marker":"[17]"}],"fun_headline_variants":["EEG connectivity shape holds steady across montages","Right-skewed EEG weights: a stable brain signature","Volume conduction shapes EEG weight uniformity","Montage and measure don't sway EEG weight skew"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing assumption is that every connection weight can be treated as a number in [0,1] when its distribution is binned for Shannon entropy; two of the coupling measures, the imaginary part of coherency and amplitude envelope correlation, can produce negative values, and the paper never states how those negatives were folded into the analysis.","fun_headline_variants_meta":{"raw":{"variants":["EEG connectivity shape holds steady across montages","Right-skewed EEG weights: a stable brain signature","Volume conduction shapes EEG weight uniformity","Montage and measure don't sway EEG weight skew"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000521,"raw_usage":{"total_tokens":2581,"prompt_tokens":1067,"completion_tokens":1514,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":683,"completion_tokens_details":{"reasoning_tokens":1455}},"tokens_in":683,"tokens_out":1514,"duration_ms":12031,"temperature":1.0,"reasoning_tokens":1455,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-10T20:43:18.509548+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Recompute skewness, kurtosis, and Shannon entropy for the simulated imaginary-coherence and amplitude-envelope-correlation networks after an explicit nonnegative transformation such as taking absolute values or shifting weights to [0,1]; if the right skew, kurtosis below 3, or entropy ranges change materially, the claimed independence from coupling measure is an artifact of the missing handling step.","supporting_citations":[{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Supplies the multicenter normative EEG cross-spectra used to validate the simulated distribution findings."},{"cited_title":"NeuroImage","cited_arxiv_id":null,"evidence_quote":"Supplies the real intracranial EEG signals used as cortical sources in the forward simulation."},{"cited_title":"150, 1–16 (2023)","cited_arxiv_id":null,"evidence_quote":"Provides the boundary-element forward solver used to compute scalp EEG from cortical sources."},{"cited_title":"NeuroImage","cited_arxiv_id":null,"evidence_quote":"Defines the phase-lag index, the volume-conduction-robust measure contrasted with coherence-based measures."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Defines amplitude envelope correlation, one of the volume-conduction-sensitive coupling measures."},{"cited_title":"How do the resting EEG preprocessing states affect the outcomes of postprocessing?","cited_arxiv_id":"2310.15194","evidence_quote":"Introduces Shannon entropy as the uniformity measure for network connection weight distributions."}],"review_version":1}