{"id":"ab8eed4c-ea2b-42e6-bebb-cdbf7f2348ed","arxiv_id":"2507.01247","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":4.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"The Probabilistic Visibility Graph extends the visibility graph with exponentially weighted connections over obstructed points, and its network measures differ between rest and anesthesia ECoG data.","lead":"This paper introduces the Probabilistic Visibility Graph (PVG), a new way to turn a time series into a network by adding probabilistic links between points that block each other in the classic visibility graph. The authors argue the PVG better captures long-range patterns and show it separates rest and anesthesia brain recordings.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Central rest/anesthesia contrast is not shown to be robust to the PVG's free parameters; the ECoG P0 value is unreported and no sensitivity analysis is provided.","rationale":"The reader's weakest assumption correctly identifies the arbitrary exponential form of Eq. (4) and the free parameters rho and P0 as the soft spot. I agree that this is the most load-bearing concern because the entire empirical demonstration reduces to comparing network metrics that are sensitive to these choices. The paper even demonstrates in Fig. 2 that L, C, and k_max vary dramatically with rho and P0, so the claim that rest/anesthesia differences are meaningful requires showing they are stable across reasonable parameter ranges. The omission of the P0 value used in the ECoG analysis is a concrete reproducibility gap that directly undermines the central claim. The lack of statistical testing is also relevant, but it is secondary: even with significance tests, an unreported threshold and no sensitivity analysis would leave the interpretation ambiguous. The proposed test would settle the matter by checking whether the rest-vs-anesthesia ordering is invariant. If it is, the concern is resolved and the conditional acceptance stands; if not, the claim would need to be substantially weakened. The paper has some merits: the PVG is clearly defined, the simulation illustrates the intended long-range connectivity, and the use of a small-worldness measure normalized by random networks is a reasonable first step. However, no code or data release is mentioned, which is an additional transparency issue. On balance, the verdict remains CONDITIONAL pending the parameter-robustness check and reporting of the exact choices used.","tokens_in":7012,"tokens_out":7746,"duration_ms":93535,"concrete_test":"On the same ECoG segments, re-compute sigma (Eq. 10) and the degree-distribution exponent gamma for a grid of P0 values (e.g., 0.01, 0.1, 0.5, 0.9) and rho values spanning the Fig. 3 range, and repeat with two alternative probability functions, e.g., P_ij = (1 + rho h_max)^-1 and P_ij = exp(-rho h_max^2). Record the sign of (sigma_rest - sigma_anesthesia) and (gamma_rest - gamma_anesthesia) across all settings, and report the P0 actually used in the paper. If the sign reverses or loses significance on any reasonable setting, the central claim is parameter-dependent rather than robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central empirical claim—rest shows stronger small-worldness and scale-free structure than anesthesia—rests on graph metrics computed from the PVG adjacency matrix, whose edges are defined by two unconstrained user parameters: the decay rate rho in Eq. (4) and the threshold P0 in Eq. (8). The ECoG analysis (Sec. 2.3) never reports the P0 value used and provides no sensitivity analysis for P0, despite Fig. 2 showing that L, C, and k_max change sharply with both rho and P0. Because P_ij = exp(-rho h_max) is posited solely by analogy to quantum tunnelling and is not fitted or validated, an equally plausible decay function could reorder the rest/anesthesia curves. Thus the headline distinction may be an artifact of a particular arbitrary thresholding scheme rather than a stable property of the data. The paper's own Fig. 3 plots show all metrics as functions of rho, but without a P0 grid or alternative models, the robustness of the ordering is unknown.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces the Probabilistic Visibility Graph (PVG), an extension of the classical Visibility Graph in which nodes are connected with probability P_ij = exp(-rho h_max), where h_max is the maximum obstruction height and rho is a decay parameter; a threshold P0 converts these probabilities into a binary adjacency matrix. The authors test the method on a simulated amplitude-modulated signal, showing how network measures L, C, and k_max vary with rho and P0, and on macaque ECoG recordings under rest and anesthesia, reporting that rest exhibits higher clustering, stronger small-worldness, and more scale-free degree distributions than anesthesia. The central claim is that the PVG captures both local and global temporal patterns better than the classical VG, thereby offering a tool for analyzing multiscale time series.","tokens_in":7265,"tokens_out":4008,"duration_ms":48859,"significance":"If the empirical claims are supported, the PVG would be a useful, easily implementable extension of the visibility-graph family, and the simulation part of the paper is transparent and plausible. The main value would be in providing a tunable way to interpolate between purely local visibility and dense global connectivity. However, the ECoG-based conclusions are currently not supported by statistical inference, depend on unreported user-chosen thresholds, and rely on a crude power-law fitting procedure. These issues must be addressed before the paper can substantiate its headline claims about neural-state differences or about superior long-range dependency capture.","major_comments":[{"comment":"The value of P0 used in the ECoG analysis is never reported. Since the binary adjacency matrix A_PVG is defined by thresholding P_ij at P0, and Fig. 2 shows that L, C, and k_max change sharply with P0, the rest/anesthesia differences in Fig. 3 may depend strongly on this choice. The authors should state the P0 value and provide a sensitivity analysis over P0 (e.g., a grid of P0 values in Fig. 3 or in a supplementary figure) to demonstrate that the reported ordering is stable.","section":"Sec. 2.3, Eq. (8)"},{"comment":"The claim that rest has \"significantly higher\" small-worldness than anesthesia is not supported by any statistical test. The shaded areas in Fig. 3 indicate standard deviations across 30 segments, but no paired test, permutation test, bootstrap confidence interval, or multiple-comparison correction is reported. Since the paper's central empirical claim is a difference between two brain states, inferential statistics are required to distinguish a stable effect from sampling variability.","section":"Sec. 2.3, Fig. 3"},{"comment":"The scale-free claim rests on a linear regression of the log-transformed degree distribution, but the fitting range (k_min), binning procedure, goodness-of-fit, confidence intervals, and comparison to alternative distributions (e.g., log-normal or stretched exponential) are omitted. The text's criterion gamma > 1 is too weak to identify scale-free behavior, and the more restrictive criterion 2 < gamma < 3 is not applied. The authors should report fitted exponents with uncertainty and use a more rigorous power-law testing procedure.","section":"Sec. 2.3, Fig. 3(f)"},{"comment":"The exponential decay P_ij = exp(-rho h_max) is introduced by analogy to quantum tunnelling and is not derived from the data or compared with alternative functional forms. Because the main empirical contrast is computed on graphs generated by this specific choice plus user-selected rho and P0, the authors should either provide a data-driven justification for the exponential form or demonstrate that the rest/anesthesia differences are robust to plausible alternative decay functions (e.g., power-law or linear decay). This is a concrete correctness-risk concern rather than a claim of circularity.","section":"Eq. (4)"},{"comment":"The claim that the PVG is superior to the classical VG in capturing long-range dependencies is based primarily on the maximum degree k_max, which trivially increases when the graph becomes denser. The comparison between k_max (up to 5000) and the autocorrelation-derived lag (3852) does not directly measure whether long-range dependencies in the time series are captured. The authors should validate the method on a ground-truth simulation with known long-range coupling, for example by computing the correlation between PVG connection probability and the true coupling strength.","section":"Sec. 2.2"}],"minor_comments":[{"comment":"The caption for Fig. 3 labels panel (b) as \"Average degree,\" while the text in Sec. 2.3 refers to \"network density.\" These are different quantities; the authors should make the terminology consistent.","section":"Fig. 3 caption and Sec. 2.3"},{"comment":"In the sentence \"Both rest and anesthesia conditions demonstrated small-world properties with rest showing significantly higher sigma than the rest condition,\" the phrase \"than the rest condition\" should read \"than the anesthesia condition.\"","section":"Sec. 2.3"},{"comment":"There is a potential inconsistency between the weighted matrix M_ij = W_ij * P_ij and the binary adjacency matrix A_PVG, which is defined by P_ij >= P0. If W_ij = 0 (e.g., equal values), then M_ij = 0 even though A_PVG,ij = 1. The authors should clarify which matrix is used for each reported network measure and whether edges with zero weight are included in the binary analysis.","section":"Eqs. (7) and (8)"},{"comment":"The axis/caption description says the power-law exponent gamma is shown \"as a function of k,\" but the panels are plotted against rho. This should be corrected to \"as a function of rho.\" Also, the formula in the text \"P(k)~k−1\" appears garbled and should be written as P(k) ~ k^{-gamma}.","section":"Fig. 3(f)"},{"comment":"The paper does not provide a data or code availability statement. Since the method is computationally simple, sharing code would substantially increase reproducibility; at minimum, the threshold choices and fitting details should be specified.","section":"References and availability"}],"recommendation":"major_revision","confidential_remarks":"The method is clearly defined and the simulation part is straightforward, but the central empirical result is not yet statistically substantiated. The missing P0 value and lack of sensitivity analysis are the most serious issues; they are fixable but require additional experiments. I would not recommend rejection on novelty grounds alone, but the current manuscript does not meet the standard for a methods paper in a journal that emphasizes reproducible and statistically grounded results."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Two things to know. First, the paper does deliver a new construction: replacing the hard visibility rule with the probabilistic edge probability P_ij = exp(-rho h_max) makes the visibility graph tunable between the classical VG (P0=1) and a fully connected graph, and the method is clearly written. Second, the empirical payoff is still conditional: the rest/anesthesia separation in ECoG is the headline result, but the threshold P0 used in that analysis is never reported, and there is no sensitivity analysis showing the ordering of the conditions survives changes in P0 or in the stipulated exponential decay.\n\nThe approach is genuinely simple and the simulations behave as one would hope: increasing rho lengthens paths, lowers clustering, and shrinks the maximum degree, while smaller P0 admits more long-range edges. Applying the PVG to real ECoG data with rest and anesthesia is a reasonable first test, and the idea that anesthesia homogenizes the network is plausible.\n\nThe soft spots are real but not fatal. The main one: Figure 3 plots everything as a function of rho, but the reader cannot know which P0 produced those curves, nor whether other P0 values flip the rest/anesthesia order. Since Eq. (4) is a postulate, a different decay function could reorder the results. Second, \"rest showing significantly higher sigma\" is asserted without any statistical test; the shaded standard deviations are informative but not a test. Third, the power-law exponent is from a linear fit to log-binned degree distributions; that is a crude estimator, and the paper cites Broido and Clauset, who show that most such claims do not survive rigorous testing. Fourth, no code or data are released, so the analysis is not reproducible as it stands.\n\nIf the authors report the exact parameters, add a sensitivity sweep over P0 and perhaps the decay family, and run a simple permutation test on the ECoG contrast, the paper would be solid as a methods note. As is, it is a plausible increment, not an established one. I would send it to peer review because the method is well-defined and the application is of interest, but I would expect major revision. Good for a signal-processing audience who wants a tunable VG; skip if you need a validated biomarker. My own take: I wouldn't cite the empirical claim, but I'd keep the construction in mind.","headline":"A clearly-defined probabilistic extension of the visibility graph, but the rest/anesthesia claim needs parameter reporting and sensitivity analysis before it convinces.","tokens_in":7730,"tokens_out":2411,"would_cite":false,"duration_ms":27486,"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 Probabilistic Visibility Graph adds tunnelling-style probabilistic links to the classical visibility graph, letting it capture long-range time-series patterns and distinguish rest from anesthesia in brain recordings.","keywords":["Time-Series","Complex Networks","Visibility Graph","Probabilistic Visibility Graph","long-range dependencies","small-world network","scale-free network","electrocorticography"],"falsifier":"Re-run the ECoG rest-versus-anesthesia analysis with a different decay kernel, such as $P_{ij}=h_{\\max}^{-\\alpha}$, while matching the network density between conditions; if the small-worldness and scale-freeness separation between rest and anesthesia disappears or reverses, the claim would be shown to depend on the chosen tunnelling model rather than on the structure of the brain signals.","tokens_in":6843,"feed_emoji":"🧠","tokens_out":10439,"duration_ms":82157,"temperature":0.7,"pith_summary":"This paper introduces the Probabilistic Visibility Graph (PVG), a way of turning a time series into a network in which every pair of time points is connected with a probability that decays with the height of the intermediate values blocking the sight line, inspired by quantum tunnelling. The intent is to overcome the classical Visibility Graph's tendency to lose long-range relationships: with the PVG, distant points can still be linked, with strength tunable by a decay parameter and a threshold. The paper shows on simulated amplitude-modulated signals that the PVG reaches far larger maximum degrees than the classical VG, and on macaque electrocorticography data that the PVG's network metrics distinguish rest from anesthesia, with rest showing stronger small-world and scale-free (hub-dominated) topology. If the method holds up, it offers a flexible graph-based tool for capturing cross-scale, long-range patterns in long physiological and other time series.","feed_headline":"Probabilistic graph separates rest from anesthesia in brain data","feed_subtitle":"By allowing tunnelled links through signal peaks, it catches long-range patterns the classic visibility graph misses.","key_machinery":"The load-bearing object is the probabilistic connection rule $P_{ij}=e^{-\\rho h_{\\max}}$ combined with the arctangent interaction strength $W_{ij}$ and the threshold $P_0$. The maximum obstruction height $h_{\\max}$ is the tallest vertical gap between the straight line joining two time points and the intermediate data points; when no obstruction exists, $h_{\\max}=0$ and $P_{ij}=1$. This rule is what lets the graph 'tunnel' through barriers that would block a classical visibility edge, with $\\rho$ controlling how strongly obstructions suppress long-range links and $P_0$ controlling how many weak links survive to appear in the final graph. The same machinery, varied through $\\rho$ and $P_0$, generates the full family of networks used in the simulations and the ECoG analysis.","core_discovery":"The central claim is that replacing the all-or-nothing visibility rule by a probabilistic one yields a network representation that preserves the classical local structure while adding long-range edges that carry global pattern information. Formally, after normalizing the series to $[0,1]$, the paper defines the connection probability $P_{ij}=e^{-\\rho h_{\\max}}$, where $h_{\\max}$ is the largest obstruction height between points $i$ and $j$, and merges this with the weighted-visibility interaction $W_{ij}=\\arctan((x(t_j)-x(t_i))/(t_j-t_i))$ to obtain the weighted connectivity $M_{ij}=W_{ij}P_{ij}$. A threshold $P_0$ converts $M$ into an adjacency matrix; $P_0=1$ recovers the classical VG and $P_0=0$ connects all pairs. The paper reports that on an amplitude-modulated test signal the PVG's maximum degree climbs to the theoretical maximum of about 5000, versus 56 for the classical VG, and that on ECoG data from macaques, rest exhibits higher clustering, shorter path lengths, stronger small-worldness, and scale-free degree distributions relative to anesthesia, which appears denser, more homogeneous, and less hub-dominated.","pith_inferences":["A natural extension the paper does not pursue is to test whether the rest/anesthesia separation is tied to the exponential decay form; re-running the analysis with a power-law or logistic decay kernel would show whether the reported differences are a property of the signals or of the chosen tunnelling model.","Because the AM simulation is explicitly designed to mimic phase-amplitude coupling, the PVG could be used as a network-based index of cross-frequency coupling strength, complementing spectral PAC measures.","The reported scale-free behaviour rests on a linear fit to the log-transformed degree distribution; applying stricter goodness-of-fit criteria would likely sharpen (or weaken) the claim that rest is genuinely scale-free.","The method's $O(N^2)$ cost limits direct application to very long series; approximate or hierarchical versions of the visibility check would be needed for terabyte-scale recordings."],"forward_implications":["Varying $P_0$ between 0 and 1 sweeps a family of graphs from the all-to-all network to the classical VG, so the PVG offers a tunable middle ground between local and global connectivity.","The simulated AM signal shows that the PVG captures long-range interactions that the classical VG misses, indicated by the maximum degree rising to the theoretical maximum (about 5000) instead of 56.","On real ECoG data, rest and anesthesia produce different PVG topologies: rest is small-world and scale-free (hub-dominated, short paths, high clustering) while anesthesia is denser and more homogeneous.","Network measures of the PVG vary systematically with $\\rho$ and $P_0$, so conclusions about brain-state differences must be made over a range of parameters rather than at a single setting."],"supporting_citations":[{"why":"Introduces the classical Visibility Graph whose all-or-nothing visibility rule the PVG extends.","marker":"[9]"},{"why":"Supplies the weighted visibility interaction strength $W_{ij}$ that the PVG combines with the tunnelling probability.","marker":"[13]"},{"why":"Provides the network measures (clustering, path length, density, degree) used to characterize PVG graphs.","marker":"[18]"},{"why":"Provides the macaque ECoG recordings used for the rest versus anesthesia comparison.","marker":"[19]"},{"why":"Defines the small-worldness measure $\\sigma$ used to compare the two brain states.","marker":"[21]"},{"why":"Underpins the interpretation of scale-free degree distributions and the criterion for calling a network scale-free.","marker":"[23]"},{"why":"Supplies the linear-regression method used to estimate the power-law exponent of the degree distribution.","marker":"[25]"}],"fun_headline_variants":["Probabilistic graph distinguishes rest from anesthesia","Tunnelling edges expose brain network differences in anesthesia","Quantum tunnelling graph reveals hidden links in time series","Tunnelling method finds hub-dominated brain networks at rest"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the chance of a non-visible connection should drop off exponentially with the tallest obstruction height between the two time points, and that the user-chosen decay $\\rho$ and threshold $P_0$ are the right way to balance local and global connections; if a different decay rule were used, the network topology and the reported rest versus anesthesia differences could change.","fun_headline_variants_meta":{"raw":{"variants":["Probabilistic graph distinguishes rest from anesthesia","Tunnelling edges expose brain network differences in anesthesia","Quantum tunnelling graph reveals hidden links in time series","Tunnelling method finds hub-dominated brain networks at rest"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001326,"raw_usage":{"total_tokens":5410,"prompt_tokens":974,"completion_tokens":4436,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":590,"completion_tokens_details":{"reasoning_tokens":4374}},"tokens_in":590,"tokens_out":4436,"duration_ms":102665,"temperature":1.0,"reasoning_tokens":4374,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-06T20:56:19.666258+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Re-run the ECoG rest-versus-anesthesia analysis with a different decay kernel, such as $P_{ij}=h_{\\max}^{-\\alpha}$, while matching the network density between conditions; if the small-worldness and scale-freeness separation between rest and anesthesia disappears or reverses, the claim would be shown to depend on the chosen tunnelling model rather than on the structure of the brain signals.","supporting_citations":[{"cited_title":"visible\" to each other. Visibility is determined by the geometric criterion: 𝑥(𝑡","cited_arxiv_id":null,"evidence_quote":"Introduces the classical Visibility Graph whose all-or-nothing visibility rule the PVG extends."},{"cited_title":"Weighted Visibility Graph With Complex Network Features in the Detection of Epilepsy,","cited_arxiv_id":null,"evidence_quote":"Supplies the weighted visibility interaction strength $W_{ij}$ that the PVG combines with the tunnelling probability."},{"cited_title":"A new method for quantifying the performance of EEG blind source separation algorithms by referencing a simultaneously recorded ECoG signal,","cited_arxiv_id":null,"evidence_quote":"Provides the macaque ECoG recordings used for the rest versus anesthesia comparison."}],"review_version":1}