{"id":"074f3d21-132e-4d92-a55e-18cb432a366e","arxiv_id":"2608.10862","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":3,"one_line_summary":"In a noise-driven FitzHugh-Nagumo model, localized patches form when either the instantaneous noise amplitude or its persistence crosses a threshold, with the two linked by the integrated noise strength.","lead":"This paper uses simulations of an excitable-media model to show that random fluctuations create transient localized activity patches in two ways: strong short-lived noise or weak long-lived noise. It gives cell biologists and physicists a common framework for predicting when biochemical noise makes local patches instead of quiet or system-wide activity.","discovery_kind":"extension","skeptic_critique":{"model":"deepseek-v4-flash","headline":"Phase boundaries rest on an undefined run-classification rule: the manuscript never specifies the u-threshold, minimum lifetime, or spatial extent used to score a run as noise-induced excitation, so the reported amplitude–persistence compensation is not yet reproducible or falsifiable.","rationale":"The reader's weakest_assumption identifies exactly the gap I consider most load-bearing: the missing operational definition of what counts as a noise-induced excitation. My stress-test of the full manuscript confirms that this definition is never supplied despite being the sole observable in all three phase diagrams and in the patch-property maps of Fig. 6. The paper's central assertion that amplitude and persistence are interchangeable controls is expressed through phase boundaries; boundaries without a defined classifier are not falsifiable predictions. I considered two other potential concerns: (1) the numerical scheme in Appendix A appears to add the stochastic forcing after the Crank-Nicolson deterministic step rather than inside the implicit system (Eqs. A5–A10 contain no noise term), which is at best an ambiguous operator-splitting and at worst an inconsistent integrator for the colored-noise SPDE; and (2) Appendix B's mean-field treatment is said to agree 'excellently' with simulations without showing a comparison. Both are real reproducibility issues, and the numerical ambiguity is serious enough that the authors should provide a corrected or clarified formulation and ideally release code. However, the detection-rule gap is more directly load-bearing because even a perfectly implemented simulator would still leave the phase diagrams undefined. The concrete test I propose is deliberately minimal: it requires only the raw u(ℓ,t) fields and three explicit classifiers, and it settles whether the qualitative structure of the phase diagram depends on the label assignment. I agree with the reader that a conditional verdict is appropriate: the physics is plausible and the qualitative trends are likely robust, but the missing classifier, code, and error bars prevent full acceptance. My read does not change the reader's verdict; it sharpens the reason. I therefore set verdict_should_be to UNCHANGED and agreement_with_reader to agree.","tokens_in":23285,"tokens_out":9830,"duration_ms":97017,"concrete_test":"Reanalyze the recorded activator fields u(ℓ,t) from a fixed set of simulation runs (or re-run them) using three explicitly defined classifiers: (i) any lattice site exceeds u > 0 at any time step; (ii) a spatially connected region with u > −0.5 has width at least 5% of the system and persists at least 2 τ_u; (iii) a region with u ≥ 0.9 has width at least 10% of the system and persists at least 5 τ_u. Regenerate Fig. 2 panels (a)–(c) under each classifier and compare the phase boundaries, the monotonicity of A_c(τ_c), and the location of the localized-to-alternating crossover. If the boundaries shift by more than one parameter-space grid cell or if the monotonicity in Fig. 2(b) reverses, the amplitude–persistence compensation claim is an artifact of the untested detection rule; if all three classifiers yield the same qualitative structure, the central claim is robust.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The central claim (instantaneous amplitude and temporal persistence are interchangeable nucleation controls, unified by A = σ_η^2 τ_c) is measured through the phase diagrams of Fig. 2, whose color encodes the percentage of 50 runs exhibiting \"noise-induced excitation.\" Yet the text nowhere defines the operational classifier: no threshold on u, no minimum patch lifetime, no minimum spatial extent, and no rule distinguishing a localized excitation patch from the spatially extended alternating phase. Without this criterion, the boundaries between quiescent, pattern-forming, and alternating regimes are uncomputable from the raw data. Consequences are direct: the critical integrated noise strength A_c(τ_c) in Fig. 2(b), the monotonicity claim for that boundary, and the contrasting trends in Fig. 2(a) vs. Fig. 2(c) all depend on where the detector sits. A lax detector (any site with u > 0 at any instant) would classify almost every run as excited; a strict detector (u ≈ 1 over > 10% of the system for > 20 τ_u) would suppress the pattern-forming phase entirely. Appendix C similarly reports patch size and lifetime as percentages and τ_u units, but the thresholds that make a patch a patch are absent. The associated code and data are not provided, so the reported percentages cannot be independently reconstructed. This is the single most load-bearing gap because every quantitative comparison in the paper is expressed through this undefined observable.","agreement_with_reader":"agree"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper studies a one-dimensional FitzHugh-Nagumo reaction-diffusion system driven by Ornstein-Uhlenbeck noise, with the integrated noise strength A = σ_η^2 τ_c as the primary control parameter. By sweeping the inhibitor response time τ_v, the noise correlation time τ_c, the noise amplitude σ_η, and A, the authors report three dynamical regimes: quiescent, spatially extended alternating, and pattern-forming with transient localized excitation patches. The central claim is that localized patches can be nucleated either by short-lived fluctuations with large instantaneous amplitude or by weaker fluctuations that persist longer, and that these two routes are unified through the integrated noise strength A, while the inhibitor response time determines whether an excitation remains local or spreads system-wide. The paper includes a qualitative mechanism based on threshold crossing, a mean-field treatment of the nonequilibrium quiescent background in the white-noise limit, and appendices documenting the numerical scheme and patch size/lifetime statistics.","tokens_in":23670,"tokens_out":3801,"duration_ms":38466,"significance":"If the central claim holds, the paper gives a simple and potentially useful organizing principle for noise-induced localized patterns in excitable media: amplitude and persistence of fluctuations act as joint nucleation controls, with the inhibitor time scale controlling the fate of a nucleated excitation. The phase diagrams are falsifiable predictions, and the white-noise limit result (localized patterns without temporal correlations) is a clear, nontrivial message for a broad readership. The paper also connects to concrete biological phenomena, such as Ras-PI3K patches, which increases its significance. However, the reproducibility of the quantitative results is currently compromised by an underspecified run-classification rule, the absence of error bars, and an unverified claim of excellent mean-field agreement; these gaps must be addressed before the manuscript can support its quantitative conclusions.","major_comments":[{"comment":"The phase diagrams in Fig. 2 color-code the percentage of 50 runs exhibiting \"noise-induced excitation,\" but the manuscript never defines the operational classifier: it does not state the threshold on u, the minimum spatial extent, the minimum lifetime, or the rule that distinguishes a localized excitation patch from the spatially extended alternating phase. Since the quiescent-pattern boundary in Fig. 2(a), the critical curve A_c(τ_c) in Fig. 2(b), and the contrasting trends in Fig. 2(c) are all read off this undefined observable, a different detector could shift the boundaries or even change the monotonicity of A_c(τ_c). Please specify the exact detection rule (including thresholds and any cooldown/merging conditions), and provide the detection code or a precise pseudocode description so that the amplitude-persistence compensation result is reproducible.","section":"Dynamical phases; Fig. 2"},{"comment":"Each phase point is based on 50 independent runs, but no error bars, confidence intervals, or statistical uncertainties are reported for the percentage of runs classified as excited. The white dashed phase boundaries in Fig. 2 are also introduced without a stated contouring rule or threshold percentage. For a stochastic classification, the binomial uncertainty on a 50-run percentage is sizable near the boundaries, so the monotonicity claim for A_c(τ_c) and the crossover arrows in Figs. 2(a) and 2(c) cannot currently be distinguished from detector and sampling effects. Please add error bars or at least report the classification threshold and the number of runs per point, and state how the boundary curves were constructed.","section":"Dynamical phases; Fig. 2 and Fig. 6"},{"comment":"Appendix B states that the mean-field estimates \"have excellent numerical agreement with the simulated results,\" but no comparison plot, table, or quantitative error metric is provided. Because the approximations (spatially Gaussian u, negligible covariance between u^2 and v, small δv) are introduced ad hoc, this agreement claim is the only evidence that the nonequilibrium background calculation is quantitatively reliable. Please add a direct comparison of μ_u, μ_v, and σ_u^2 against simulation results as functions of A, and state the numerical values or relative errors supporting the \"excellent agreement\" wording.","section":"Appendix B"}],"minor_comments":[{"comment":"The value of τ_u is never specified; the figure captions and parameter lists give α, β, D_u, D_v, τ_v, τ_c, A, and σ_η, but not τ_u or the time step Δt used for the production runs. Please state these values explicitly, since all reported lifetimes and correlation times are quoted in units of τ_u.","section":"Reaction-diffusion equations; Fig. 2 caption"},{"comment":"The claim that patch lifetime and size \"scale linearly with τ_v\" is supported only by visual inspection of Fig. 5. Please add linear fits with their slopes, or at least quantitative correlation measures, and include error bars on the averaged patch properties.","section":"Fig. 5 and Appendix C"},{"comment":"The statement that amplitude and persistence are \"linked through the integrated noise strength\" is true by definition because A ≡ σ_η^2 τ_c. The nontrivial empirical content is the phase behavior under the two different parameterizations in Figs. 2(a) and 2(c); the text should state explicitly that the definitional link is not itself a measured result, to avoid overstating the circularity-sensitive part of the claim.","section":"Eq. (3) and Discussion"},{"comment":"The notation in the vector term \"2βcv1\" is ambiguous because the unit vector 1 and the scalar multiplication are not defined; please clarify the notation and also report the fixed-point iteration tolerance and maximum iteration count used in the production runs.","section":"Appendix A, Eq. (A10)"}],"recommendation":"major_revision","confidential_remarks":"The manuscript is well within the scope of the journal and the qualitative message is attractive, but the missing operational definition of \"noise-induced excitation\" is the single most important obstacle: every quantitative phase boundary and the central compensation claim depend on it. I would be willing to accept after the authors specify the detection rule, add error quantification, and document the mean-field comparison. The definitional nature of A = σ_η^2 τ_c should also be acknowledged more carefully in the text."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"First, the thing to know: this paper has a real idea—parameterizing the noise by integrated strength A = σ_η² τ_c and showing that white noise alone can nucleate localized patches, with persistence acting as a second control—but the central phase diagrams are built on a run-classification rule the authors never state. That is not a minor omission; it is the instrument reading used for every boundary in Fig. 2.\n\nWhat is actually new: the systematic interpolation between white and Ornstein-Uhlenbeck noise, the explicit contrast between fixed-A and fixed-σ_η sweeps, and the demonstration that τ_v (inhibitor response) sets patch size and lifetime independently of how the noise is parameterized. The paper is honest about the relationship to Hecht et al. [47,48], and the model itself is standard FHN with additive OU noise. The mean-field appendix is crude but gives a concrete criterion (σ_u ~ (α+β−1)/α) that could be checked. The numerics use 50 runs per point; error bars are absent, but for phase diagrams of this kind that is workable if the detection rule were fixed.\n\nThe soft spots are, in order of severity. First, the missing definition of 'noise-induced excitation': no threshold on u, no minimum lifetime, no minimum spatial extent. The stress-test note is right that a lax vs strict detector would shift the boundaries and could even change the compensation claim. The authors say in the captions that colors are 'percentage of runs exhibiting noise-induced excitation,' but never say what that means operationally. Second, the appendix claims 'excellent numerical agreement' for the mean-field background without showing a comparison plot. Third, no code or data are provided; the patch statistics in Appendix C are also expressed as percentages without thresholds.\n\nThe definitional link A = σ_η² τ_c is not a circularity problem: it is a parameterization choice, and the phase diagrams are independent simulation evidence. The qualitative regimes and the contrasting trends in Figs. 2(a) and (c) are robust enough to believe, but I would not want to cite the quantitative boundary A_c(τ_c) until the detection rule is specified.\n\nFor whom: stochastic reaction-diffusion and cell-signaling modelers. It deserves a serious referee, but the referee should push hard on the operational definition and, ideally, get the code and data. My verdict: conditional accept, not reject.","headline":"Sound central idea—amplitude and persistence as joint nucleation controls—but the phase diagrams rest on an undefined run-classification rule, so the paper needs revision before it is reproducible.","tokens_in":24143,"tokens_out":2117,"would_cite":true,"duration_ms":20085,"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":"Nucleating a localized excitation needs a fixed total noise dose; amplitude and persistence can be traded.","keywords":["excitable media","FitzHugh-Nagumo","noise-induced pattern formation","temporal correlations","Ornstein-Uhlenbeck noise","integrated noise strength","localized excitation patches","inhibitor response time"],"falsifier":"Run the same model with an explicit excitation detector (for example, activator above 0.5 over at least five percent of the system for at least ten activator time units) and sweep all three parameter planes; if the quiescent-to-pattern boundary no longer follows contours of $A=\\sigma_\\eta^2 \\tau_c$ at fixed $\\tau_v$, the amplitude-persistence compensation claim fails.","tokens_in":23120,"feed_emoji":"⚡","tokens_out":9053,"duration_ms":80365,"temperature":0.7,"pith_summary":"Transient patches of activity appear spontaneously in many excitable biological systems, but it has been unclear which statistical feature of the fluctuations triggers them. This paper argues that neither instantaneous noise amplitude nor temporal persistence acts alone; the controlling quantity is the integrated noise strength $A=\\sigma_\\eta^2 \\tau_c$, the accumulated stochastic forcing. In a one-dimensional FitzHugh-Nagumo excitable medium, the same localized patch can be nucleated by a short loud fluctuation or by a longer quiet one, provided they deposit the same $A$. The simulations map out three regimes—quiescent, localized pattern-forming, and system-wide alternating—and show that the inhibitor response time $\\tau_v$ subsequently decides whether a nucleated excitation stays local or spreads. The result suggests that experiments should characterize intracellular noise by both amplitude and correlation time, not amplitude alone.","feed_headline":"Strong brief noise and weak long noise trigger the same patterns","feed_subtitle":"In excitable media, amplitude and persistence trade off; integrated noise strength sets the nucleation boundary.","key_machinery":"The machinery is a stochastic FitzHugh-Nagumo reaction-diffusion system on a periodic one-dimensional domain, driven by an Ornstein-Uhlenbeck noise field with equal-time rms amplitude $\\sigma_\\eta$ and correlation time $\\tau_c$. The load-bearing identity is the integrated noise strength $A=\\sigma_\\eta^2 \\tau_c$, defined as the time integral of the noise autocorrelation, which collapses amplitude and persistence into a single control parameter. Three complementary parameter sweeps—$\\tau_v$ versus $\\tau_c$ at fixed $A$, $A$ versus $\\tau_c$ at fixed $\\tau_v$, and $\\tau_v$ versus $\\tau_c$ at fixed $\\sigma_\\eta$—separate amplitude effects from persistence effects. The inhibitor response time $\\tau_v$ supplies the second timescale that decides whether an excitation stays localized or becomes system-wide, and a mean-field treatment of the white-noise limit yields a self-consistent estimate of the nonequilibrium quiescent background and a nucleation criterion $\\sigma_u \\sim (\\alpha+\\beta-1)/\\alpha$.","core_discovery":"The paper's central claim is that transient localized excitation patches are nucleated by accumulated stochastic forcing rather than by instantaneous amplitude or persistence separately. The identity $A=\\sigma_\\eta^2 \\tau_c$ links the two routes: a short-lived fluctuation with large equal-time rms amplitude and a longer-lived fluctuation with proportionally smaller amplitude deposit the same integrated noise strength and can cross the same excitation threshold. At fixed $A$, increasing the correlation time lowers the instantaneous amplitude and eventually suppresses nucleation; at fixed $\\sigma_\\eta$, increasing the correlation time adds persistence without the amplitude penalty and strongly promotes nucleation. The opposite trends in these two sweeps are the paper's direct evidence that amplitude and persistence are interchangeable stochastic control parameters. Once a patch is nucleated, its growth, lifetime, and whether it remains local or spreads are governed mainly by the inhibitor response time $\\tau_v$, and sufficiently persistent noise can extend a patch's life when $\\tau_c \\gtrsim \\tau_v$.","pith_inferences":["Editorial: the phase-boundary analysis implies a quantitative nucleation-rate prediction—probability per site per unit time should depend on $A$ through the variance $\\sigma_u^2$ computed in the mean-field treatment—though the paper does not derive such a rate.","Editorial: the same amplitude-persistence tradeoff may extend to non-Gaussian or spatially correlated noise if the controlling variable is still the integrated autocorrelation, but the paper does not test that case.","Editorial: because the patch-detection rule is not specified, the exact location of the quiescent-pattern boundary is convention-dependent; an explicit detector would convert the phase diagrams into a sharper falsifiable prediction."],"forward_implications":["Cells with different sources or sizes of molecular fluctuations could still show similar protrusion dynamics, as long as amplitude and persistence compensate to the same integrated noise strength.","Gaussian white noise alone can support transient localized patterns at sufficiently large $A$, so finite temporal correlation is not a prerequisite for patch formation.","Because $A$ controls nucleation while $\\tau_v$ controls spread, an excitable network can be switched from local to system-wide activity by changing only inhibitor kinetics while leaving the noise fixed.","Patch lifetime and size should increase roughly linearly with $\\tau_v$ throughout the pattern-forming regime, giving a quantitative observable for experiments.","Weak but persistent perturbations could drive an excitable signaling system across threshold with less collateral effect than a strong brief stimulus."],"supporting_citations":[{"why":"Defines the activator-inhibitor excitable equation that is the starting point of the model.","marker":"[22]"},{"why":"Provides the circuit realization of the FitzHugh-Nagumo equations used here.","marker":"[23]"},{"why":"Supplies traveling-wave solutions of nerve conduction that justify the spatial reaction-diffusion treatment.","marker":"[24]"},{"why":"Prior study of spatiotemporally correlated noise in excitable media that this work extends.","marker":"[25]"},{"why":"The standard theory of colored noise that supports the Ornstein-Uhlenbeck autocovariance and integrated noise strength.","marker":"[27]"},{"why":"Documents noise-induced wave nucleation in an excitable chemical system, the baseline phenomenon generalized here.","marker":"[41]"},{"why":"Earlier work on transient localized patterns in noise-driven reaction-diffusion systems whose strong-white-noise limitation is addressed.","marker":"[47]"},{"why":"Connects localized noise-driven patches to chemotactic cell motility, the biological context motivating the study.","marker":"[48]"}],"fun_headline_variants":["Noise amplitude and persistence trade off to nucleate patterns","Integrated noise strength, not amplitude alone, gates pattern formation","Weak persistent noise matches strong brief noise in excitable media","Amplitude and persistence: two routes to the same noise threshold"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"All three phase diagrams rely on an unstated operational rule for what counts as a noise-induced excitation—no activator threshold, minimum lifetime, or spatial extent is specified—so a different detection rule would move the reported phase boundaries.","fun_headline_variants_meta":{"raw":{"variants":["Noise amplitude and persistence trade off to nucleate patterns","Integrated noise strength, not amplitude alone, gates pattern formation","Weak persistent noise matches strong brief noise in excitable media","Amplitude and persistence: two routes to the same noise threshold"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.001161,"raw_usage":{"total_tokens":4782,"prompt_tokens":895,"completion_tokens":3887,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":511,"completion_tokens_details":{"reasoning_tokens":3818}},"tokens_in":511,"tokens_out":3887,"duration_ms":26439,"temperature":1.0,"reasoning_tokens":3818,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-12T15:31:57.324861+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run the same model with an explicit excitation detector (for example, activator above 0.5 over at least five percent of the system for at least ten activator time units) and sweep all three parameter planes; if the quiescent-to-pattern boundary no longer follows contours of $A=\\sigma_\\eta^2 \\tau_c$ at fixed $\\tau_v$, the amplitude-persistence compensation claim fails.","supporting_citations":[{"cited_title":"Busch and F","cited_arxiv_id":null,"evidence_quote":"Prior study of spatiotemporally correlated noise in excitable media that this work extends."},{"cited_title":"Nagumo, S","cited_arxiv_id":null,"evidence_quote":"Provides the circuit realization of the FitzHugh-Nagumo equations used here."},{"cited_title":"Rinzel and J","cited_arxiv_id":null,"evidence_quote":"Supplies traveling-wave solutions of nerve conduction that justify the spatial reaction-diffusion treatment."},{"cited_title":"FitzHugh, Impulses and physiological states in the- oretical models of nerve membrane, Biophys","cited_arxiv_id":null,"evidence_quote":"Defines the activator-inhibitor excitable equation that is the starting point of the model."},{"cited_title":"H¨ anggi and P","cited_arxiv_id":null,"evidence_quote":"The standard theory of colored noise that supports the Ornstein-Uhlenbeck autocovariance and integrated noise strength."},{"cited_title":"Beato, I","cited_arxiv_id":null,"evidence_quote":"Documents noise-induced wave nucleation in an excitable chemical system, the baseline phenomenon generalized here."},{"cited_title":"Hecht, D","cited_arxiv_id":null,"evidence_quote":"Earlier work on transient localized patterns in noise-driven reaction-diffusion systems whose strong-white-noise limitation is addressed."},{"cited_title":"Hecht, M","cited_arxiv_id":null,"evidence_quote":"Connects localized noise-driven patches to chemotactic cell motility, the biological context motivating the study."}],"review_version":1}