{"id":"586f6658-c382-4626-85c4-e63f6c489cf5","arxiv_id":"2502.06057","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"high","formal_verification":"none","parameter_count":7,"one_line_summary":"The q parameter fitted to EEG event intervals is proposed as a neural-complexity measure; it declines with age and correlates with theta and beta power, but the evidence is weakened by potential confounds.","lead":"This paper tests whether a parameter called q, borrowed from Tsallis statistical mechanics and fitted to EEG wave patterns, can serve as a measure of brain complexity in 70 adults across seven mental states. It finds that q decreases with age and tracks theta and beta brain-wave power, but the analysis does not rule out that q is simply a repackaged version of the EEG power spectrum.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The q–theta/q–beta1 correlations are not separated from the EEG power spectrum, so the central claim that q measures neural complexity is not yet supported.","rationale":"The reader's weakest assumption is exactly the load-bearing issue: the paper assumes q reflects neural complexity independently of the EEG spectral composition, and the q–band correlations may be a mathematical consequence of the event definition. My reading agrees. The paper is transparent and reports a useful dataset, but the central interpretation requires an explicit control separating q from the power spectrum. The proposed surrogate test is the direct and minimal check that would settle the concern. Since the reader already assigned a CONDITIONAL verdict with this concern identified, my stress-test does not move the verdict.","tokens_in":20068,"tokens_out":4027,"duration_ms":45022,"concrete_test":"Phase-randomized surrogate control: for each subject, functional state, and channel, compute the FFT of the artifact-cleaned EEG, randomize the phases while preserving the amplitude spectrum, and inverse-transform. Apply the identical threshold-crossing event definition, class binning, PDR-interval removal, and q-fit pipeline to each surrogate. Then recompute the q–theta and q–beta1 correlations across subjects. If the surrogate correlations fall inside the empirical confidence intervals (resting open-eyes: r ≈ 0.48 for theta, r ≈ −0.25 for beta1), then q is determined by the power spectrum and the paper's interpretation of q as neural complexity is not supported. If the surrogate correlations are zero or much weaker, the concern is refuted and the empirical correlations gain neurophysiological specificity.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's central claim is that q, fitted to threshold-crossing interval distributions, is a valid measure of neural complexity (NC). The load-bearing support includes q–theta positive and q–beta1 negative correlations (Table 3, Figure 8), the AllCh-vs-single-channel difference (Table 1), and the age correlation (Table 2). The weakest point is that q is estimated from intervals between downward crossings of a −1 SD threshold (Data Processing and Curve Fitting). For any stationary signal, that interval distribution is directly shaped by the autocorrelation function, and hence by the power spectrum. A theta-dominant signal produces long, clustered intervals; a beta-dominant signal produces short, regular intervals. The observed q–theta and q–beta1 correlations may therefore be a restatement of the spectral content used to construct the events, not evidence about neural complexity. The paper provides no surrogate analysis, no partial correlations controlling for band powers, and no comparison with established complexity measures. The AllCh result is also vulnerable: pooling interval distributions from heterogeneous channels broadens the distribution and can raise the fitted q even if channels are independent, so q_AllCh > mean q_single does not by itself demonstrate nonlocal correlations. The age correlation, while a useful external anchor, is also known to track spectral slowing and cannot resolve the confound. Without a control that separates q from the power spectrum, the central claim is not independently supported.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The manuscript applies Tsallis q-statistics to EEG threshold-crossing interval distributions in 66 adults across seven functional states, estimating a q parameter for all channels pooled and per channel. The authors report four main findings: q is higher for all channels pooled than for the average of single channels; q is negatively correlated with age; functional states modulate q locally but not globally; and q is positively correlated with theta power and negatively with beta1 power. They interpret q as a measure of neural complexity and claim the results support q-statistics as a first approach to describing human brain complexity.","tokens_in":20373,"tokens_out":2319,"duration_ms":24645,"significance":"If the interpretation were fully supported, the paper would offer a relatively simple, computationally light EEG complexity index that tracks age and spectral correlates of integration, with potential clinical applications in ADHD and other neuropsychiatric conditions. The study has strengths: a reasonably sized sample (66 adults), seven well-defined functional states, openly described fitting equations and bounds, and supplementary datasets. However, the central inference that q measures neural complexity independently of the power spectrum is not established by the analyses presented, because the event intervals used to estimate q are threshold crossings of the same signal whose band powers are then correlated with q. The q–theta/q–beta1 correlations, the AllCh-versus-single-channel difference, and even the age effect can all be reproduced by spectral content alone under plausible null models. The paper would need surrogate-data or partial-correlation controls, or comparisons with established complexity measures, before its main claim can be accepted as evidence rather than as a restatement of spectral composition.","major_comments":[{"comment":"The q parameter is estimated from the distribution of intervals between downward crossings of a −1 SD threshold of the EEG signal. For a stationary signal, the distribution of threshold-crossing intervals is determined by the autocorrelation function and hence by the power spectrum. A theta-dominant signal will produce longer, more clustered intervals, while a beta-dominant signal will produce shorter, more regular intervals. The reported positive correlation between q and theta power and negative correlation with beta1 power may therefore be a mathematical consequence of the event definition rather than evidence about neural complexity. The manuscript provides no surrogate data analysis, no partial correlations controlling for band powers, and no comparison with other complexity measures. Since the abstract's central claim rests on these correlations, this confound is load-bearing and needs to be addressed.","section":"Data Processing and Curve Fitting; Spectral Composition and Complexity (Table 3, Figure 8)"},{"comment":"The finding that q(AllCh) is higher than the mean q of single channels is interpreted as evidence of nonlocal correlations. However, pooling interval distributions from 20 heterogeneous channels broadens the pooled distribution relative to each channel's distribution, which can raise the fitted q even if the channels are independent stationary processes. The analysis as presented does not control for this pooling artifact; for example, the authors do not compare the observed AllCh q with q obtained by pooling independent realizations from a single channel, or with a shuffled-channel surrogate. Without such a control, Table 1 does not by itself support the hierarchical-complexity interpretation.","section":"Complexity (Table 1)"},{"comment":"The negative correlation between q and age is offered as external validation of q as a complexity measure. Since q is correlated with theta and beta1 power, and EEG spectral composition slows with age, the age–q correlation may be mediated entirely by the same spectral confound identified above. The manuscript does not report partial correlations of q with age after controlling for band powers, nor does it show that the age effect survives such controls. The age correlation is therefore not currently an independent anchor for the construct validity of q.","section":"Results, Sample and Table 2"},{"comment":"The exclusion procedure for AllCh fits is described as visual inspection of convergence, with 35 EEG signals of specific functional states excluded, yet Table 1 reports N = 66 for every state. The relationship between the reported N and the exclusions is unclear; if the 35 exclusions are distributed across states, the effective sample sizes in Tables 1–3 need to be stated per state. More importantly, visual post hoc exclusion of non-convergent fits can bias q estimates and inflate correlations. The authors should report the number of excluded cases per state, provide quantitative convergence criteria, and ideally rerun the main analyses with alternative exclusion rules.","section":"Results, Sample and Table 1"}],"minor_comments":[{"comment":"The phrase 'applied to the ongoing and EEG and its spectral power' appears to contain a typo; it should likely read 'applied to the ongoing EEG and its spectral power'.","section":"Abstract"},{"comment":"The text states amplitudes are 'truncated at amplitudes of 100mV'; since EEG amplitudes are in microvolts, this should be '100 µV' (and likewise for the negative threshold description).","section":"Data Processing and Curve Fitting"},{"comment":"In the sentence reporting theta power differences, 't-stat=2.40m' appears to contain a typographical artifact; it should be 't-stat=2.40'.","section":"Results, Complexity"},{"comment":"The ADHD screening scale is referred to as 'ARSR' in the text but is commonly abbreviated 'ASRS'; the abbreviation should be corrected for consistency with the cited instrument.","section":"Experimental Procedures"},{"comment":"'alfa' should be spelled 'alpha' for consistency with the band nomenclature used elsewhere, and 'teta' should be 'theta'.","section":"Table 3"}],"recommendation":"major_revision","confidential_remarks":"The central claim is interesting and the authors are clearly expert in q-statistics, but the manuscript currently treats the q–spectral correlations as neurophysiological findings without ruling out the much simpler statistical explanation that threshold-crossing interval distributions are shaped by the power spectrum. The missing surrogate/control analyses are standard and should be feasible with the existing data. If the authors can show, for example, that q–theta associations survive phase-randomized or spectral-flattened surrogates and partial correlations, the paper would make a solid contribution. I would not recommend rejection because the confound is potentially fixable within the scope of the manuscript, but the current version is not yet sufficient to support the abstract's claim."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Dear colleague,\n\nHere's my read of arXiv:2502.06057. It's a legitimate extension of the same group's earlier q-EEG work (refs 21, 23) to a 70-adult sample across seven functional states. The genuinely new pieces are the q–theta positive and q–beta1 negative correlations across states, the local q modulations (e.g., occipital drop with eyes closed), and the age correlation, which replicates a well-known complexity finding. Data handling is careful: artifact suppression, band-specific fits, and supplementary tables for most analyses. The local/global distinction is also worth taking seriously.\n\nThe soft spot is the one the stress-test note flags. q is fitted to intervals between downward crossings of a −1 SD threshold, and that interval distribution is directly shaped by the signal's autocorrelation function, which is to say its spectrum. A theta-dominant signal gives long, clustered intervals; a beta-dominant signal gives short, regular ones. So the q–theta and q–beta1 correlations may be a restatement of the spectral content rather than evidence about neural complexity. The paper offers no surrogate analysis, no partial correlations controlling for band power, and no comparison with an independent complexity measure (LZ, sample entropy, multiscale entropy). The AllCh-vs-single-channel contrast has the same problem: pooling heterogeneous interval distributions can inflate q without implying nonlocal correlations. That point is asserted, not tested.\n\nI also think the post hoc exclusion of 35 AllCh fits (roughly 7.5% of the AllCh state-subject fits) is more than cosmetic. The paper says they lacked \"visible convergence,\" but without a sensitivity analysis we don't know whether including them flips any of the main correlations. The age/q correlation is the most robust result, but it is exactly the one that could be explained by spectral slowing, so it doesn't rescue the interpretation.\n\nNone of this makes the paper sloppy. It reads as an honest exploratory report, with transparent exclusions and raw data available on request. But the abstract's final sentence—\"These findings support the idea that... q-statistics can describe the human NC\"—goes a step beyond what the evidence currently supports. With surrogate controls (e.g., phase-randomized or spectrally matched signals) and partial correlations, the claim could be made to work. Right now it is conditional.\n\nI'd send it to peer review, because the dataset and method deserve careful referee time and the confound is fixable. I wouldn't cite it as evidence for q-as-complexity until the control analyses appear.\n\nBest,\n\n[Your name]","headline":"Useful exploratory extension of the authors' own q-EEG method, but the q–spectrum correlations are not yet separated from the threshold-crossing event-definition confound, so the complexity claim outruns the controls.","tokens_in":20900,"tokens_out":2301,"would_cite":false,"duration_ms":22612,"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 the q parameter of q-statistics, fitted to EEG event-interval distributions, is a valid first-approach measure of human neural complexity, supported by higher q for pooled channels, declining q with age, and q's…","keywords":["q-statistics","neural complexity","electroencephalogram","event-interval distribution","theta band","beta band","aging","functional states"],"falsifier":"Take the real EEG segments, randomize the Fourier phases while preserving the power spectrum, rebuild the signal, and apply the same threshold-crossing event definition and q fit; if the surrogate q values reproduce the original q values and the same theta/beta correlations, then q is not measuring complexity beyond spectral content.","tokens_in":19864,"feed_emoji":"🧠","tokens_out":10172,"duration_ms":83450,"temperature":0.7,"pith_summary":"This paper tries to establish that the index $q$ of $q$-statistics—a generalization of Boltzmann–Gibbs statistical mechanics in which $q$ measures the non-additivity of entropy—can serve as a first-pass measure of human neural complexity when fitted to EEG event-interval distributions. The authors fitted $q$ to ongoing EEG from 70 adults across seven functional states, both at 20 individual scalp channels and for all channels pooled into one distribution. They found that pooled-channel $q$ is higher than the average of single-channel $q$, that $q$ declines with age, and that $q$ correlates positively with theta-band power and negatively with beta1-band power. The authors interpret this pattern as evidence that $q$ captures system-level, non-local complexity of brain activity rather than a property of any single site, and they propose $q$-statistics as a viable way to describe human neural complexity.","feed_headline":"EEG q parameter rises for whole-brain activity and falls with age","feed_subtitle":"A single fitted value tracks neural complexity: pooled channels outrank single ones, and theta power tracks q.","key_machinery":"The central object is the parameter $q$ of the $q$-exponential distribution used by $q$-statistics, fitted to the empirical distribution of time intervals between EEG events. An event is defined as the signal amplitude crossing down through a threshold of $-1.0$ standard deviation of the negative part of the signal, and intervals from 80 to 120 ms—the $\\alpha$-band Posterior Dominant Rhythm—are removed before fitting. The fitted function is $y = a x^c / [1+(q-1)b x^h]^{1/(q-1)}$, where $q=1$ recovers the ordinary Boltzmann–Gibbs exponential and $q>1$ produces the heavier tails that the paper associates with long-range correlations and non-additive entropy. The machinery does the argument by converting a messy, high-dimensional EEG into one scalar per recording (per channel or per pooled cloud), whose statistical behavior can then be compared across ages, functional states, and spectral bands.","core_discovery":"The central claim is that $q$-statistics can describe human neural complexity. Using the $q$-exponential distribution fitted to the intervals between threshold-crossing events in the EEG, the paper reports three converging findings: $q$ is higher when all 20 channels are pooled than when single-channel $q$ values are averaged, $q$ is negatively correlated with age at the global level (most strongly in resting open-eyes, $r=-0.50$), and $q$ is positively correlated with theta-band power and negatively with beta1-band power across states and channels. The authors also find that functional states do not change pooled $q$, while single-channel $q$ responds to states in anatomically sensible ways, such as lower posterior $q$ with eyes closed and higher posterior $q$ during preferred music. On the strength of these patterns, the paper concludes that, as a first approach, $q$-statistics can describe human neural complexity.","pith_inferences":["An extension the paper does not perform: phase-randomize each EEG segment to preserve its power spectrum while destroying temporal structure; if $q$ and its theta/beta correlations survive, then $q$ is carrying spectral information rather than complexity.","Because the theta/beta1 ratio shows the strongest correlation with $q$ in the paper's table, a practical extension is to test whether that ratio alone can predict $q$ in new data; if it can, the distinct contribution of $q$ as a complexity measure would need re-evaluation.","The paper's own dissociation between theta power and $q$ in the Oddball state suggests $q$ may index the integration or informativeness of oscillations rather than their amplitude; a targeted test would compare $q$ across two states matched for theta power but differing in task complexity."],"forward_implications":["If $q$ is a valid complexity measure, then one fitted scalar per EEG recording can summarize system-level neural complexity without source reconstruction or explicit connectivity estimation.","The negative age correlation implies $q$-statistics could be used to track age-related changes in brain complexity in longitudinal or clinical settings.","The positive $q$–theta and negative $q$–beta1 correlations imply that complexity in this measurement is carried by slow, integrative oscillations rather than by fast, local processing.","The stable pooled $q$ across functional states, alongside state-dependent single-channel $q$, implies that global complexity may index stable individual characteristics while local subsystems reconfigure during tasks.","The higher pooled-channel $q$ relative to averaged single-channel $q$ implies that whole-brain complexity is non-additive, consistent with long-range correlations across scalp sites."],"supporting_citations":[{"why":"Supplies the original derivation of q-statistics and the q-exponential form that the paper fits to EEG interval distributions.","marker":"[14]"},{"why":"Establishes q as an index of complexity in non-additive systems, which is the theoretical bridge to neural complexity.","marker":"[13]"},{"why":"Introduces the method of fitting q-exponentials to EEG event-interval distributions, the approach this study extends.","marker":"[21]"},{"why":"Shows that the (q, c) parameters distinguish ADHD from typical EEGs, motivating q as a sensitive measure of mental-profile differences.","marker":"[23]"},{"why":"Provides the theta-gamma coupling account that supports interpreting the positive q-theta correlation as long-range integration.","marker":"[5]"},{"why":"Reviews theta oscillation functional correlates that back the link between theta power and integrative, high-order processing.","marker":"[7]"},{"why":"Defines the EEG bands, electrode placement, and the alpha Posterior Dominant Rhythm that the paper removes before fitting.","marker":"[24]"},{"why":"Documents that physiologic complexity decreases with aging, the baseline finding that the negative q-age correlation builds on.","marker":"[32]"},{"why":"Supports the interpretation of beta-band activity as stabilizing current states, consistent with the negative q-beta1 correlation.","marker":"[79]"}],"fun_headline_variants":["Whole-brain EEG fits beat single channels in complexity metric","Age erodes, theta boosts EEG q-complexity index","Pooled EEG channels yield higher q, and age lowers it","q-statistics peek at neural complexity: global > local, theta-linked","Neural complexity via EEG q: whole brain wins, age subtracts"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that q measures neural complexity itself rather than just EEG spectral composition, because the intervals q is fitted to are defined by threshold crossings whose frequency is directly shaped by low-frequency power, and the paper does not separate q from the power spectrum.","fun_headline_variants_meta":{"raw":{"variants":["Whole-brain EEG fits beat single channels in complexity metric","Age erodes, theta boosts EEG q-complexity index","Pooled EEG channels yield higher q, and age lowers it","q-statistics peek at neural complexity: global > local, theta-linked","Neural complexity via EEG q: whole brain wins, age subtracts"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000174,"raw_usage":{"total_tokens":1337,"prompt_tokens":1052,"completion_tokens":285,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":668,"completion_tokens_details":{"reasoning_tokens":197}},"tokens_in":668,"tokens_out":285,"duration_ms":3584,"temperature":1.0,"reasoning_tokens":197,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T16:52:32.537600+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Take the real EEG segments, randomize the Fourier phases while preserving the power spectrum, rebuild the signal, and apply the same threshold-crossing event definition and q fit; if the surrogate q values reproduce the original q values and the same theta/beta correlations, then q is not measuring complexity beyond spectral content.","supporting_citations":[{"cited_title":"International Journal of Psychophysiology, 157:82-99 (2020)","cited_arxiv_id":null,"evidence_quote":"Reviews theta oscillation functional correlates that back the link between theta power and integrative, high-order processing."},{"cited_title":"Possible generalization of Boltzmann-Gibbs statistics","cited_arxiv_id":null,"evidence_quote":"Supplies the original derivation of q-statistics and the q-exponential form that the paper fits to EEG interval distributions."},{"cited_title":"Introduction to Nonextensive Statistical Mechanics – Approaching a Complex World","cited_arxiv_id":null,"evidence_quote":"Establishes q as an index of complexity in non-additive systems, which is the theoretical bridge to neural complexity."},{"cited_title":"M., Lima, H","cited_arxiv_id":null,"evidence_quote":"Shows that the (q, c) parameters distinguish ADHD from typical EEGs, motivating q as a sensitive measure of mental-profile differences."},{"cited_title":"L., editors","cited_arxiv_id":null,"evidence_quote":"Defines the EEG bands, electrode placement, and the alpha Posterior Dominant Rhythm that the paper removes before fitting."},{"cited_title":"L., Peng, C","cited_arxiv_id":null,"evidence_quote":"Documents that physiologic complexity decreases with aging, the baseline finding that the negative q-age correlation builds on."}],"review_version":1}