{"id":"0eeee969-1251-455a-a056-404e023adb78","arxiv_id":"2502.05814","paper_version":2,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":5,"one_line_summary":"A topological time-frequency framework applies STFT to average birth and death values from graph filtrations of sliding-window fMRI connectivity, then correlates the resulting spectrograms with intelligence scores.","lead":"The paper combines persistent homology with short-time Fourier transforms to turn dynamic brain connectivity into time-frequency spectrograms of topological features. It reports weak correlations between these spectrograms and fluid and crystallized intelligence in HCP resting-state fMRI data.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The scalar summaries b(t) and d(t) collapse the whole graph-filtration barcode to two means, and the simulation validates full persistence barcodes, not the STFT pipeline; the reported intelligence correlations may reflect mean edge-weight dynamics rather than topology.","rationale":"The paper's central methodological contribution is the STFT of topological summaries. My concern is not that averaging is never useful; it is that the paper provides no evidence that these particular averages preserve the topology-dependent signal. The existing simulation compares full persistence barcodes to clustering, which is a different pipeline. A control replacing b(t) and d(t) with mean correlation is cheap and decisive: if the intelligence correlations survive, the 'topological' part of the spectrogram is not responsible; if they vanish, the averages carry genuine topological information. The 116/379 inconsistency and the uncorrected significance threshold are additional revision items, but the averaging/validation gap is the most load-bearing because it questions what the spectrogram actually measures. I therefore keep the reader's CONDITIONAL verdict: the method is plausible but needs this control before the central claim can be credited.","tokens_in":6966,"tokens_out":10631,"duration_ms":121230,"concrete_test":"Re-run the Figure 5/6 analysis on the HCP data with b(t) and d(t) replaced by the mean of all sliding-window correlation coefficients, using identical STFT parameters and the same subject set, and compare the resulting intelligence-correlation maps to the published ones. If the maps are highly similar (e.g., Spearman correlation above 0.9 between the two sets of frequency-resolved correlations, or the same bands exceed the |r|=0.2 threshold), then the topological decomposition adds no discriminative information beyond mean edge weight; if the maps diverge, the scalar summaries retain topology-specific signal.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim requires that the STFT of b(t) and d(t) tracks topological dynamics of the brain network. But Section II.B.2 defines b(t) and d(t) as arithmetic means over q0 = p-1 birth values and q1 = (p-1)(p-2)/2 death values. With p = 379, d(t) averages over 71,253 non-MST edges per time point; even with p = 116 it averages over 6,555. Averaging discards which edges enter the MST and which non-MST edges create which cycles, so two networks with identical mean MST weight and identical mean non-MST weight but different modularity or cycle organization produce identical inputs to the STFT. The claimed 'multi-scale topological features' are therefore not actually multi-scale in topology: persistence-scale information is collapsed into two scalars. The validation in Section II.B.3 does not test this pipeline. It applies 2-Wasserstein distance to the full sorted lists of birth and death values for static circular point clouds, which preserves exactly the distributional information that b(t) and d(t) remove. No experiment shows that the scalar summaries, or their spectrograms, separate topologically different dynamic networks. Consequently the reported 0D-stable/1D-nonstationary pattern and the intelligence correlations in Figures 5-6 could be produced by any slowly varying measure of mean connectivity, such as the mean correlation coefficient, and attributed to topology without support. An additional unresolved inconsistency compounds this: the Methods state AAL 116 parcels while Results state 379x379 matrices, so it is unclear which p, and thus which q0 and q1, define the summaries.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper proposes a framework that combines graph-filtration persistent homology with the short-time Fourier transform (STFT) to analyze dynamic functional brain connectivity. For each sliding-window correlation matrix, the authors compute the average 0D birth value b(t) and the average 1D death value d(t), then compute STFT spectrograms of these two scalar time series. The method is applied to resting-state fMRI data from 400 HCP participants, with reported findings that 0D topology is stable across time while 1D topology is non-stationary, and that the topological spectrogram shows weak correlations with fluid and crystallized intelligence. A simulation on circular point clouds is used to argue that topological Wasserstein-distance clustering produces fewer false positives than k-means or hierarchical clustering.","tokens_in":7239,"tokens_out":6454,"duration_ms":62559,"significance":"If the central claims were fully supported, the proposal would be a useful addition to dynamic functional connectivity analysis: it would convert graph filtrations into a time-frequency representation and suggest that 0D/1D topological summaries carry cognitive information. The paper builds on previously published graph-filtration results [1,17,19], and the genuinely new element is the STFT of scalar birth/death summaries plus the HCP application. The authors are also correct that frame-wise comparisons of resting-state dynamics are statistically problematic. However, as written, the validation does not exercise the proposed pipeline, and several internal inconsistencies need to be resolved before the claims can be accepted. No code or data availability statement is provided, which further limits reproducibility.","major_comments":[{"comment":"The central validation does not test the proposed pipeline. Equations (3)-(4) reduce the persistence barcode to two scalar means b(t) and d(t); with p=379, d(t) is the mean of 71,253 death values per time point, and this averaging removes which edges form the MST and which non-MST edges create which cycles. The simulation in Section II.B.3, however, uses the 2-Wasserstein distance on the full sorted birth and death lists of static circular point clouds, preserving exactly the distributional information that b(t) and d(t) discard. No experiment demonstrates that the scalar summaries, or their STFT spectrograms, separate topologically different dynamic networks or track topological changes over time. The reported 0D-stable/1D-nonstationary pattern and the intelligence correlations in Figures 5-6 could therefore be reproduced by any slowly varying measure of mean edge weight; the paper needs a control analysis (e.g., comparing against mean correlation dynamics or random-edge-shuffle nulls) and a simulation that applies Equations (3)-(4) to time-varying networks with known topology.","section":""},{"comment":"The data dimension is ambiguous. Section II.A states that AAL parcellation yields 116 time series, but Section III reports 1173 time-varying correlation matrices of size 379 x 379 for each subject. Since q0 and q1 in Equation (3) depend on p, the effective number of nodes must be stated consistently. Please correct the parcellation description or the matrix size, and report the actual p used in the analysis.","section":""},{"comment":"The simulation result is internally inconsistent: the text first reports that topological clustering showed 37% fewer false positives than k-means/hierarchical clustering, then, a few lines later, claims a 47-50% reduction for the same comparison. With only five networks per pattern, the accuracy values carry large uncertainty; please reconcile the numbers, report per-condition results, and provide confidence intervals or resampling-based intervals.","section":""},{"comment":"The significance threshold is mis-stated and the multiple-comparison problem is not addressed. For n=374, |r|=0.2 gives t≈3.94 on 372 degrees of freedom, whose one-sided p-value is far below 0.0018. Conversely, p=0.0018 corresponds to |r|≈0.15. Moreover, correlations are evaluated over many frequency bins and two homology dimensions with no correction for multiple testing; the phrase 'statistically significant but weak' in the captions of Figures 5 and 6 needs a defensible multiple-testing procedure (e.g., FDR or permutation over subject labels).","section":""},{"comment":"The claim that 0D topology is stable while 1D topology is non-stationary is supported only by a single-subject spectrogram and an unsupported sentence that the pattern appears in all 400 subjects. A claim about stationarity should be quantified across subjects, e.g., with a test for time-variation of the PSD in each frequency band, or at least group-level summary statistics of b(t) and d(t). Without such evidence, the abstract's statement that the method identifies 0D and 1D features that are robust to noise and temporal misalignments is not established.","section":""}],"minor_comments":[{"comment":"The PSD equations PB(τ,ω)=20 log10 B(τ,ω) and PD(τ,ω)=20 log10 D(τ,ω) use the complex STFT directly; they should use |B| and |D| (or squared magnitudes) before taking logarithms.","section":""},{"comment":"The abstract says features are identified 'in the signal's time-frequency domain'; the actual pipeline computes STFT of topological summaries, not persistent homology on the time-frequency representation. Please rephrase to avoid ambiguity.","section":""},{"comment":"The STFT parameters are underspecified: 'window size equivalent to 10% of total signal duration' needs the number of samples and the overlap in samples; 'FFT length set to the next power of two greater than the window size' should be stated numerically.","section":""},{"comment":"The number of subjects for the intelligence correlations differs between Figure 5 (400 subjects) and Figure 6 (374 subjects), but the text says 'in 374 subjects' for both analyses; please clarify the exact sample size for each correlation.","section":""},{"comment":"There are several typographical errors: 'weighted weighted network' in the Fig. 1 caption, 'brain netework' in Section III, and 'topological data dnalysis' in reference [14].","section":""}],"recommendation":"major_revision","confidential_remarks":"To the editor: The manuscript's core proposal is interesting, but the current evidence does not yet establish that the spectrogram of b(t) and d(t) is a topological measure rather than a mean-connectivity measure. The internal inconsistencies (116 vs 379 nodes; 37% vs 47-50%) suggest that the manuscript needs careful revision before it can be considered further. The heavy reliance on the authors' previous papers is not itself disqualifying, but the novelty relative to reference [19] should be clarified; Sections II.B.1 largely restate prior published decomposition results, and the new STFT step is the only novel methodological element."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"This paper grafts a short-time Fourier transform onto Chung and colleagues' earlier topological embedding for dynamic brain networks. That specific combination is new, and the writing is clear. The graph-filtration birth/death decomposition is solid and rests on published mathematical results. Using the time-varying mean birth and death values as input to an STFT is a reasonable thing to try, and the spectrograms are a compact way to visualize mean connectivity dynamics.\n\nThe soft spots are real and not minor. The summaries b(t) and d(t) are arithmetic means over all maximum-spanning-tree edges and all non-tree edges. With the 379-node matrices used in the results, d(t) averages 71,253 values per time point; even at 116 nodes it is 6,555. That collapses the persistence barcode to two scalars and throws away which edges form which cycles at which scale. Two networks with identical mean MST weight and identical mean non-MST weight but different modularity or cycle organization feed identical input to the STFT. So the claim of \"multi-scale topological features\" is not supported by the construction.\n\nThe validation does not help. The simulation compares full sorted birth/death lists using 2-Wasserstein distance, which preserves exactly the distributional information that b(t) and d(t) remove. No experiment shows that the scalar summaries, or their spectrograms, separate topologically different dynamic networks. The intelligence correlations are exploratory, weak (threshold at r=0.2 with no multiple comparison correction), and could just as easily be driven by mean edge-weight dynamics. There are also internal contradictions: Methods says AAL 116 parcels, Results report 379x379 matrices; simulation says false-positive reduction of 37% in one section and 47-50% in another. These are fixable, but they affect the computation itself, not just the prose.\n\nWho is this for? Readers interested in TDA applied to resting-state fMRI might find it a digestible preliminary sketch. It is not yet a validated method. The idea is worth pursuing, but the evidence as presented does not back the strength of the claims. I would send it to peer review rather than desk reject—the novelty is real and the problems are addressable—with instructions that the authors either validate the actual STFT pipeline against meaningful topological contrasts or reframe the claims around mean connectivity dynamics.","headline":"A new but unvalidated pipeline—STFT of scalar birth/death means—with internal inconsistencies and a simulation that tests the wrong thing.","tokens_in":7800,"tokens_out":2651,"would_cite":false,"duration_ms":25746,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["55N31"],"pacs":[],"model":"deepseek-v4-flash","headline":"A short-time Fourier transform of two scalar topological summaries extracted from sliding-window brain networks yields a topological spectrogram in which 0D topology is stable and 1D topology is non-stationary, and this spectrogram…","keywords":["persistent homology","time-frequency analysis","graph filtration","functional brain networks","topological spectrogram","resting-state fMRI","short-time Fourier transform","birth-death decomposition"],"falsifier":"Randomly permute the edges within each time point's maximum spanning tree (and separately within the non-tree edges) so that the average birth and death values are preserved while the temporal identity of each edge is destroyed, then recompute the spectrogram and its correlations with intelligence; if the correlations survive, the scalar summaries carry only average edge weight rather than topology.","tokens_in":6727,"feed_emoji":"🧠","tokens_out":8732,"duration_ms":81990,"temperature":0.7,"pith_summary":"The paper sets out to turn the topology of a moving brain network into a time-frequency signal. For each sliding-window correlation network, it decomposes edge weights into 0D births and 1D deaths, averages them into two scalar time series $b(t)$ and $d(t)$, and runs a short-time Fourier transform to make a topological spectrogram. On 400 resting-state fMRI subjects, the 0D spectrogram is stable and low-frequency while the 1D spectrogram fluctuates more, and both show weak but statistically significant correlations with fluid and crystallized intelligence. The motivation is that this bypasses the need to align frames across subjects, since resting-state dynamics are asynchronous. Simulation results argue that topological clustering with the Wasserstein distance produces far fewer false positives than Euclidean k-means or hierarchical clustering on topologically equivalent shapes.","feed_headline":"Fourier transform of brain network topology tracks intelligence","feed_subtitle":"Two scalar summaries of brain-network shape produce spectrograms whose low-frequency power weakly tracks fluid and crystallized IQ.","key_machinery":"The load-bearing object is the graph-filtration birth-death decomposition $W = B \\cup D$ with $B \\cap D = \\emptyset$: for a weighted graph, sorting and deleting edge weights yields nested subgraphs, and each edge is either the birth value $b_{(i)}$ of a 0D connected component (together forming the maximum spanning tree) or the death value $d_{(i)}$ of a 1D loop. Taking per-time-point averages $b(t)$ and $d(t)$ embeds each dynamic network as a point in a 2D topological plane, and the short-time Fourier transform of those scalar series is the spectral engine that produces the topological spectrogram and the intelligence correlations.","core_discovery":"The paper claims that every weighted graph carries a unique topological decomposition of its edge weights: the sorted edge-deletion filtration splits the edges into a birth set $B$ (the edges of the maximum spanning tree, which create 0D connected components) and a death set $D$ (the remaining edges, which close and kill 1D loops). Averaging these values at each time point produces two scalar time series, $b(t)$ and $d(t)$, and the authors' central move is to pass these through the short-time Fourier transform to obtain a topological spectrogram. On resting-state fMRI data, the 0D spectrogram shows stable power concentrated below 0.03 Hz, interpreted as a persistent tree-like backbone, while the 1D spectrogram includes more variable, higher-frequency content, interpreted as cycles forming and dissolving. The spectrogram's power correlates weakly but statistically significantly with fluid and crystallized intelligence, with 1D topology showing correlations over a broader frequency range than 0D; simulation results further claim that Wasserstein-based topological clustering produces fewer false positives than Euclidean k-means or hierarchical clustering on topologically equivalent patterns.","pith_inferences":["A testable consequence the paper leaves implicit: if $b(t)$ and $d(t)$ are truly sufficient, then replacing them with quantiles or full persistence barcodes should preserve or sharpen the intelligence correlations rather than destroy them.","A permutation control that shuffles maximum-spanning-tree edge weights across time while keeping their mean fixed would reveal whether the spectrogram reflects topology or simply time-varying average connectivity; the paper does not report such a control.","The same pipeline could be moved to EEG or MEG, where temporal alignment across subjects is even harder, to see whether the stable-0D/unstable-1D split reproduces; the authors name epilepsy and Alzheimer's disease as future clinical targets."],"forward_implications":["If the central claim is correct, dynamic resting-state networks can be studied without frame-wise alignment across subjects, because the topological summaries depend on within-subject evolution rather than simultaneous instants.","The stable low-frequency 0D band would imply that a maximum-spanning-tree backbone persists over time and across individuals, serving as a common scaffold for faster cyclic dynamics.","The 1D spectrogram's broader frequency range would imply that loops form and dissolve on fast timescales, and the correlation pattern would connect recurrent network activity to fluid intelligence.","In the simulation results, the topological Wasserstein distance would be the better tool for clustering topologically defined shapes, cutting false positives by roughly half relative to Euclidean k-means and hierarchical clustering."],"supporting_citations":[{"why":"Supplies the birth-death decomposition of graph edge weights and the 2-Wasserstein distance used to compare topological summaries.","marker":"[1]"},{"why":"Provides the short-time Fourier transform formulation the spectrogram is built on.","marker":"[4]"},{"why":"Supplies the resting-state fMRI data from 400 participants that the analysis is run on.","marker":"[8]"},{"why":"Provides the preprocessing and the dynamically-changing correlation matrix model yielding the sliding-window networks.","marker":"[11]"},{"why":"Defines the graph filtration sequence of nested subgraphs used to extract birth and death values.","marker":"[13]"},{"why":"Establishes topological clustering with the Wasserstein distance that the simulation validation compares with k-means and hierarchical clustering.","marker":"[17]"},{"why":"Motivates the dynamic topological analysis of functional brain networks that this work extends into the frequency domain.","marker":"[19]"}],"fun_headline_variants":["Brain topology spectrograms track IQ","Topological time-frequency maps of brain activity link to intelligence","Persistent homology spectrograms reveal IQ correlations","Brain's topological shape in time-frequency predicts intelligence","Topological spectrograms of brain activity track IQ"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that averaging all 0D birth values and all 1D death values into two scalar time series preserves the topologically informative content of the brain network; if that averaging washes out the structure that matters, the spectrogram and its reported correlations are not really about topology.","fun_headline_variants_meta":{"raw":{"variants":["Brain topology spectrograms track IQ","Topological time-frequency maps of brain activity link to intelligence","Persistent homology spectrograms reveal IQ correlations","Brain's topological shape in time-frequency predicts intelligence","Topological spectrograms of brain activity track IQ"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000843,"raw_usage":{"total_tokens":3637,"prompt_tokens":874,"completion_tokens":2763,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":490,"completion_tokens_details":{"reasoning_tokens":2691}},"tokens_in":490,"tokens_out":2763,"duration_ms":18682,"temperature":1.0,"reasoning_tokens":2691,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-08T17:50:15.761090+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Randomly permute the edges within each time point's maximum spanning tree (and separately within the non-tree edges) so that the average birth and death values are preserved while the temporal identity of each edge is destroyed, then recompute the spectrogram and its correlations with intelligence; if the correlations survive, the scalar summaries carry only average edge weight rather than topology.","supporting_citations":[{"cited_title":"Chung, C.G","cited_arxiv_id":null,"evidence_quote":"Supplies the birth-death decomposition of graph edge weights and the 2-Wasserstein distance used to compare topological summaries."},{"cited_title":"Durak and O","cited_arxiv_id":null,"evidence_quote":"Provides the short-time Fourier transform formulation the spectrogram is built on."},{"cited_title":"Van Essen, S.M","cited_arxiv_id":null,"evidence_quote":"Supplies the resting-state fMRI data from 400 participants that the analysis is run on."},{"cited_title":"Huang, S.-T","cited_arxiv_id":null,"evidence_quote":"Provides the preprocessing and the dynamically-changing correlation matrix model yielding the sliding-window networks."},{"cited_title":"Lee, M.K","cited_arxiv_id":null,"evidence_quote":"Defines the graph filtration sequence of nested subgraphs used to extract birth and death values."},{"cited_title":"Songdechakraiwut and M.K Chung","cited_arxiv_id":null,"evidence_quote":"Establishes topological clustering with the Wasserstein distance that the simulation validation compares with k-means and hierarchical clustering."},{"cited_title":"Chung, S","cited_arxiv_id":null,"evidence_quote":"Motivates the dynamic topological analysis of functional brain networks that this work extends into the frequency domain."}],"review_version":1}