{"id":"fd970e15-f22e-453d-a193-3ae230213183","arxiv_id":"2605.25295","paper_version":1,"verdict":"UNVERDICTED","confidence":"LOW","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"Recursive inverse transform sampling using asymptotic first-passage distributions accelerates simulation of the first k arrival times for diffusing particles, extended to arbitrary time-dependent emission profiles.","lead":"The paper introduces simulation algorithms that generate the fastest arrival times among many diffusing particles by using known short-time asymptotic distributions instead of full trajectory tracking. This targets computational bottlenecks in modeling rare fast events in molecular systems with large particle counts.","discovery_kind":"new_method","skeptic_critique":{"model":"grok-4.3","headline":"Accuracy of inverse-transform sampling from short-time asymptotics for order statistics under prolonged emission lacks explicit error control","rationale":"The reader's weakest assumption correctly isolates the reliance on short-time asymptotics. The additional load-bearing point is that the iterative extension for time-dependent profiles inherits this reliance without a separate error analysis, which is the precise place where the claim could fail for the full range of emission profiles advertised. Because the paper supplies an implementable algorithm and asymptotic mean estimates, the appropriate adjustment is CONDITIONAL rather than outright rejection; the concrete Monte-Carlo comparison would settle whether the iteration preserves accuracy.","tokens_in":1691,"tokens_out":416,"duration_ms":13899,"concrete_test":"For the 3D Brownian motion case with constant emission rate over [0,T] where T is 10× the mean first-passage time, generate 10^4 realizations of the fastest arrival time both with the iterative algorithm and with direct Monte-Carlo trajectory simulation (using the same random seed sequence); if the sample means differ by more than 3 standard errors the iterative construction fails to control error.","verdict_should_be":"CONDITIONAL","load_bearing_attack":"The central construction uses short-time first-passage asymptotics (typically of the form P(τ < t) ∼ C t^α exp(−β/t) or similar) inside an inverse-transform sampler to generate the k-th arrival time without trajectories. For instantaneous emission this is direct; for general emission profiles the paper replaces the constant rate with an iterative integral equation whose kernel is built from the same short-time tail. Because the relevant arrival times for the extreme order statistics remain in the short-time regime only when the emission is rapid, the iterative scheme for slow or prolonged emission implicitly extrapolates the asymptotic tail into a regime where higher-order corrections (or the full series) may matter. No explicit remainder estimate or convergence proof for the iteration is supplied, so it is unclear whether the generated order statistics remain accurate once the emission timescale exceeds the diffusion timescale to the target.","agreement_with_reader":"agree"},"referee_report":{"model":"grok-4.3","summary":"The manuscript develops accelerated simulation algorithms for order statistics of extreme first-passage arrival times of diffusing particles to localized absorbing targets. It exploits short-time asymptotic first-passage distributions to derive a recursive inverse-transform sampler for instantaneous emission and extends the method to general time-dependent emission profiles through an iterative integral-equation scheme; asymptotic estimates for the mean fastest arrival time are also supplied.","tokens_in":1874,"tokens_out":393,"duration_ms":23890,"significance":"If the algorithms are shown to be accurate, the framework could deliver substantial computational gains over full-trajectory Monte Carlo methods when the number of particles is large, with direct relevance to spatial reaction networks and diffusion-controlled activation. The explicit use of known short-time asymptotics for Brownian motion in 1–3 dimensions is a constructive feature.","major_comments":[{"comment":"The iterative scheme that replaces the constant emission rate with an integral equation whose kernel is built from the short-time tail is introduced without an explicit remainder estimate or convergence analysis. When the emission timescale becomes comparable to or longer than the diffusion timescale, the generated order statistics may leave the regime where the leading asymptotic is uniformly accurate, yet no quantitative control on the resulting error is supplied.","section":"extension to time-dependent emission profiles"},{"comment":"The central efficiency and accuracy claims rest on the inverse-transform procedure, yet the manuscript contains no numerical experiments, error tables, or direct comparisons against full-trajectory simulations that would allow assessment of the method’s performance across the claimed range of emission profiles.","section":"implementation and validation"}],"minor_comments":[{"comment":"Notation for the emission profile and the iterative kernel should be introduced with a single, self-contained definition rather than being redefined piecewise.","section":"preliminaries"}],"recommendation":"major_revision","confidential_remarks":null},"author_rebuttal":{"model":"grok-4.3","summary":"We thank the referee for the constructive review and the recommendation of major revision. Below we respond point-by-point to the major comments, indicating the changes we will make to the manuscript.","responses":[{"response":"We thank the referee for highlighting the lack of remainder estimates. The iterative scheme solves the integral equation for the cumulative distribution of arrival times by successive substitution of the leading short-time asymptotic kernel; this is motivated by the fact that the fastest arrivals, which determine the extreme order statistics, occur in the short-time regime where the asymptotic is accurate. We agree that explicit error control would strengthen the presentation. In the revision we will add a dedicated paragraph discussing the truncation error induced by retaining only the leading asymptotic term, together with a heuristic bound derived from the next-order correction in the known first-passage expansion, and we will explicitly delineate the regime (emission timescale much shorter than the typical diffusion time to the target) in which the approximation remains uniformly valid.","revision_made":"partial","referee_comment":"[extension to time-dependent emission profiles] The iterative scheme that replaces the constant emission rate with an integral equation whose kernel is built from the short-time tail is introduced without an explicit remainder estimate or convergence analysis. When the emission timescale becomes comparable to or longer than the diffusion timescale, the generated order statistics may leave the regime where the leading asymptotic is uniformly accurate, yet no quantitative control on the resulting error is supplied."},{"response":"We agree that numerical validation is essential to substantiate the efficiency and accuracy claims. Although the manuscript derives the recursive inverse-transform sampler and the iterative extension in full detail, it does not contain explicit simulation results. In the revised version we will insert a new section (approximately 3–4 pages) that reports Monte Carlo comparisons: (i) instantaneous emission in 1D–3D domains, (ii) several time-dependent emission profiles (constant, exponential, and pulsed), and (iii) tables of relative error in the first k order statistics together with wall-clock time ratios versus full-trajectory Brownian simulations. These experiments will cover the parameter ranges stated in the paper and will quantify both statistical accuracy and computational speedup.","revision_made":"yes","referee_comment":"[implementation and validation] The central efficiency and accuracy claims rest on the inverse-transform procedure, yet the manuscript contains no numerical experiments, error tables, or direct comparisons against full-trajectory simulations that would allow assessment of the method’s performance across the claimed range of emission profiles."}],"tokens_in":1318,"tokens_out":531,"duration_ms":23482,"standing_objections":[]},"desk_editor":{"model":"grok-4.3","letter":"The core contribution is a recursive inverse-transform procedure that draws the k-th arrival time directly from the short-time first-passage tail instead of simulating every particle trajectory. For constant-rate emission the recursion is straightforward; for time-dependent emission the authors replace the constant with an iterative integral equation whose kernel re-uses the same asymptotic. This targets exactly the setting where full Monte Carlo becomes prohibitive: large particle counts in bounded domains with localized targets.\n\nThe approach is useful because the short-time asymptotics for Brownian motion in one, two, and three dimensions are already standard and independently derived. If those tails are accurate in the regime of interest, the sampler avoids the O(N) cost per realization. The extension to arbitrary emission profiles is the part that is not routine.\n\nThe main weakness is the one flagged in the stress test. When emission is slow or prolonged, the relevant extreme arrivals can leave the short-time window where the leading asymptotic holds. The iteration then implicitly continues the tail beyond its proven range, yet the manuscript supplies no remainder estimate, no convergence analysis for the iteration, and no numerical comparison against full-trajectory runs. Without those checks the efficiency claim cannot be quantified and the accuracy for prolonged emission remains an assumption.\n\nThe work is aimed at researchers who already use first-passage asymptotics in molecular biology or reaction networks and need faster sampling of extremes. A reader looking for a turnkey black-box method will find the dependence on pre-existing asymptotics a limitation.\n\nI would send the paper to peer review. The algorithmic idea is concrete and the computational motivation is real; a referee can request the missing validation and error control, which are straightforward to add.","headline":"The paper gives a recursive inverse-transform sampler for order statistics of extreme first-passage times that extends from instantaneous to general emission profiles, but the iterative version for slow emission rests on unverified extrapolation of short-time asymptotics.","tokens_in":2344,"tokens_out":426,"would_cite":false,"duration_ms":23923,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"grok-4.3","headline":"A recursive inverse-transform method generates order statistics of first arrival times from short-time asymptotics without simulating particle paths.","keywords":["first-passage times","order statistics","inverse transform sampling","diffusion processes","simulation algorithms","extreme value statistics","bounded domains","emission profiles"],"falsifier":"Apply the algorithm to a one-dimensional interval where exact first-passage distributions are known, generate the first k arrivals, and compare the resulting empirical distribution against the exact order statistics obtained from full Monte Carlo trajectory simulation; significant systematic deviation would falsify the method.","tokens_in":2603,"feed_emoji":"⏱","tokens_out":707,"duration_ms":19080,"temperature":0.7,"pith_summary":"The paper introduces a simulation framework that generates the first k arrival times of diffusing particles to a localized target by sampling directly from asymptotic first-passage distributions. This replaces the need to generate full trajectories for every particle, which becomes prohibitive when particle numbers are large. The approach begins with instantaneous emission and extends iteratively to arbitrary time-dependent emission profiles. It also supplies asymptotic formulas for the mean of the fastest arrival time. The method targets diffusion in bounded domains where short-time asymptotics are known, such as Brownian motion in one, two, or three dimensions.","feed_headline":"Algorithm samples fastest arrivals from asymptotics alone","feed_subtitle":"Recursive inverse transform generates order statistics of diffusion arrival times without trajectory simulation for large particle counts.","key_machinery":"Recursive inverse-transform sampling from the cumulative distribution built on short-time first-passage asymptotics, extended iteratively for time-dependent emission.","core_discovery":"We present a general simulation framework for efficiently generating order statistics of arrival times by exploiting asymptotic first-passage distributions. This framework applies to diffusion processes in bounded domains with localized absorbing targets, for which short-time first-passage asymptotics are available. Starting with the case of instantaneous emission, we derive and implement a recursive inverse transform algorithm to simulate the first k arrivals without tracking particle trajectories. We extend this algorithm to time-dependent emission profiles via an iterative approach, enabling the simulation of extreme statistics in systems with temporal injection, ranging from rapid to pro","pith_inferences":["The method could be tested for robustness by checking how the generated statistics behave when the target is moved or the domain shape is altered while keeping the same asymptotic form.","It opens the possibility of coupling the arrival-time generator to deterministic reaction equations inside the domain without resolving every diffusion path.","Accuracy for late-order statistics might degrade if the asymptotic tail does not capture the full distribution, suggesting a hybrid switch to exact sampling once the remaining particles are few."],"forward_implications":["The algorithm produces the first k arrivals directly from the asymptotic law without generating individual Brownian paths.","An iterative extension allows the same procedure to handle arbitrary time-dependent emission profiles.","Asymptotic expressions for the mean of the fastest arrival time follow from the same short-time analysis.","The resulting samples can be fed directly into models of spatial reaction networks or rare-event detection."],"fun_headline_variants":["Asymptotics enable simulation of fastest arrivals only","Recursive method samples arrival orders from distributions","No trajectories required for extreme diffusion arrival stats","Inverse transform for first k arrivals in bounded domains","Time-dependent emissions handled in accelerated first-passage sim"],"cache_read_input_tokens":2112,"weakest_assumption_plain":"The short-time first-passage asymptotics remain accurate enough to serve as the basis for inverse-transform sampling across all emission profiles and order statistics considered.","fun_headline_variants_meta":{"raw":{"variants":["Asymptotics enable simulation of fastest arrivals only","Recursive method samples arrival orders from distributions","No trajectories required for extreme diffusion arrival stats","Inverse transform for first k arrivals in bounded domains","Time-dependent emissions handled in accelerated first-passage sim"]},"model":"grok-4.3","cost_usd":0.005837,"raw_usage":{"total_tokens":2781,"prompt_tokens":677,"num_sources_used":0,"completion_tokens":59,"cost_in_usd_ticks":58374500,"prompt_tokens_details":{"text_tokens":677,"audio_tokens":0,"image_tokens":0,"cached_tokens":256},"completion_tokens_details":{"audio_tokens":0,"reasoning_tokens":2045,"accepted_prediction_tokens":0,"rejected_prediction_tokens":0}},"tokens_in":677,"tokens_out":59,"duration_ms":16456,"temperature":1.0,"reasoning_tokens":2045,"cache_read_input_tokens":256,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-06-29T23:19:17.122901+00:00","model_set":{"reader":"grok-4.3"},"falsifier":"Apply the algorithm to a one-dimensional interval where exact first-passage distributions are known, generate the first k arrivals, and compare the resulting empirical distribution against the exact order statistics obtained from full Monte Carlo trajectory simulation; significant systematic deviation would falsify the method.","supporting_citations":[],"review_version":1}