Abstract. Zero-sum Dynkin games under Poisson constraints, where players can only stop at the event times of a Poisson process, have been studied widely in the recent literature. The constraint can be modeled in two ways: either both players share the same Poisson process (the common constraint) or each player has their own Poisson process (the independent constraint). In a Markovian framework, where payoffs are functions of an underlying diffusion, we establish necessary and sufficient conditions for the equivalence of the game’s solution—comprising the value function and optimal stopping sets—under the common and independent constraints. Specifically, if the stopping sets of the maximizer and minimizer in the game under the common constraint are disjoint, then the solution to the game is the same under both the common and the independent constraint. However, the fact that the stopping sets are disjoint in the game under the independent constraint, is not sufficient to guarantee that the solution of the game under the independent constraint is also the solution under the common constraint. To demonstrate the broad applicability of our results, we solve infinite-horizon Dynkin games satisfying the assumptions of our main theorems, using backward stochastic differential equation (BSDE) techniques. This requires extending standard BSDE results from the finite-horizon setting to the infinite-horizon case, allowing for unbounded solutions.

Modelling state-level crash fatalities by a network-constrained inhomogeneous poisson point process

Abstract The conjectured three generic local bulk statistics amongst all non-Hermitian random matrix symmetry classes have recently been extended to three generic local edge statistics. We study analytically and numerically complex spacing ratios and nearest-neighbour (NN) spacing distributions that characterise such local statistics. We choose the three simplest representatives of these universality classes, given by the Gaussian ensembles of complex Ginibre, complex symmetric and complex self-dual matrices, denoted by class A, AI † and AII † . In the first part, we analytically study the complex spacing ratio in class A, at finite matrix size N . Introducing a conditional point process, we simplify existing expressions and show why an uncontrolled approximation introduced earlier converges well in the large- N limit in the bulk. When specifying to the elliptic Ginibre ensemble, we present a parameter-dependent N = 3 surmise for the complex spacing ratio, interpolating to that of the Gaussian unitary ensemble, where such a surmise is very accurate. In the second numerical part, we compare complex spacing ratios, its moments, and NN spacing distributions for all three ensembles with that of uncorrelated points, the two-dimensional (2D) Poisson process, both in the bulk and at the edge. The varying degree of repulsion within these different edge universality classes can be well understood in terms of an effective 2D Coulomb gas description, at different values of inverse temperature β . We find indications that the complex spacing ratio does not fully unfold the local statistics at the edge. Finally we verify that for small argument, in all three symmetry classes the NN spacing distributions in the bulk and at the edge are consistent with the universal cubic repulsion.

The study commenced with a discrete model of signal flow in signalling pathways based on a system of sequential, one-step, irreversible reactions with unknown kinetics and governed by a linear master equation. Building upon this, a continuous, non-linear model was created with a (1+1)-dimensional, integro-differential, space- and time-dependent wave equation that describes signal flow as a non-local, spatiotemporal, chirped envelope, dissipative solitary wave X(s,t) with two-phase hyperbolic up- and down-chirps. The phase and group velocities, and the group delay and dispersion, were determined. Transitions within the temporal and spatial profiles of X(s,t) were shown to be governed by inhomogeneous or homogeneous Poisson processes, respectively. The spatial profile represents a novel and hitherto unexploited tool for investigating signalling pathways. The energy characteristics of both profiles were determined and applied to signalling pathways that target I κ B kinase activity in macrophages and T-bet transcription factor expression in T helper cells.

Efficient patient management in hospitals requires adaptive decision-making under time-varying demand and dynamic service environments. This study proposes a heterogeneous medical patient queueing model that integrates reinforcement learning with stochastic queue dynamics to minimize overall patient waiting time. The model distinguishes between two categories of service providers (SPs): those attending first-time patients and those serving returning patients. Each category may differ in service rate but not in medical specialty. Patient arrivals follow a non-homogeneous Poisson process (NHPP) to capture realistic time-dependent flow variations. A Q-learning framework with a supervised ε-greedy policy is developed to determine optimal operational actions, such as adding or reallocating service providers, based on system state and event type. Separate Q-tables are maintained for arrival and departure events to account for differing cost and reward dynamics. Simulation results demonstrate that the proposed model significantly reduces total waiting time and system cost compared with conventional homogeneous queue models. This approach provides a data-driven mechanism for dynamic hospital queue management and can be extended to broader healthcare resource optimization scenarios.

Predictive Modelling of Pitting Corrosion in Stainless Steel Using a NonStationary Poisson Process and a Diffusion-Controlled Growth Mechanism

Classic recombination experiments designed to test genetic and environmental treatments do not directly measure chromosomal exchange, instead rates and distribution of crossing-over in F1 meiocytes are inferred from genetic markers in F2 adults. In Drosophila melanogaster females this procedure introduces substantial "missing data problems" because 75% of meiotic chromatids segregate to polar body nuclei and another 11% are transmitted to inviable F2 zygotes which cannot be scored for recombination. To address these sources of uncertainty and bias, we extend the Cx(Co)m data-generating process by assuming: 1) programmed double strand breaks occur as a Poisson point process, 2) crossover maturation is a stationary renewal process, 3) chromosome segregation is random one-half thinning of this process, 4) fertilization by X- versus Y-bearing sperm is mendelian, and 5) egg-to-adult survival is binomially distributed with a rate parameter determined by F2 marker alleles. To quantify experimental mortality, we performed egg counts for 6-point X chromosome testcrosses and marker-free X chromosome controls on identical genetic backgrounds under standard laboratory conditions. The 19,927 fly dataset revealed 44% F2 experimental mortality, and likelihood ratio tests support a model where 36 of those 44% are due to sex-specific, marker-associated viability defects. Variability in X chromosome genetic map lengths with experimental mortality can be simulated, and we provide case-control 80% power curves to guide experimental design. We propose that differential mortality should be the de facto null hypothesis when comparing F2 recombinant fractions, and we provide probabilistic models of the data-generating process to improve characterization of F1 meiotic crossover patterning.

Likelihood-based inference for three-dimensional Poisson point processes requires numerical approximation of the integral term in the log-likelihood through a cubature scheme algorithm. The quality of this approximation, and hence the accuracy of the resulting statistical inference, depends on a small set of tuning parameters controlling the cubature construction. Despite their practical importance, the literature provides little guidance on how these parameters should be selected in order to obtain reliable first-order inference. This paper addresses this issue for purely spatial three-dimensional Poisson point process models. We formalize the cubature scheme in R 3 and conduct an extensive simulation study across multiple Poisson process scenarios, process sizes, and cubature configurations. Cubature settings are evaluated by combining parameter mean squared error with a second-order diagnostic based on the three-dimensional inhomogeneous K-function and the Global Envelope Test. The simulation results are then aggregated into empirically grounded practical recommendations for selecting the dummy-point ratio, the tessellation resolution, and the dummy-point layout. Finally, a real three-dimensional spatial application illustrates how cubature choices consistent with these recommendations can lead to stable parameter estimates, reliable fitted intensities, and satisfactory diagnostic performance.

Researchers across different fields, including but not limited to ecology, biology, and healthcare, often face the challenge of sparse data. Such sparsity can lead to uncertainties, estimation difficulties, and potential biases in modeling. Here we introduce a novel data augmentation method that combines multiple sparse time series datasets when they share similar statistical properties, thereby improving parameter estimation and model selection reliability. We demonstrate the effectiveness of this approach through validation studies comparing Hawkes and Poisson processes, followed by application to subjective pain dynamics in patients with sickle cell disease (SCD), a condition affecting millions worldwide, particularly those of African, Mediterranean, Middle Eastern, and Indian descent.

There is a growing synergy between the lines of research on cycles in epilepsy and seizure forecasting. It has been conjectured, for instance, that incorporating information about significant seizure cycles into forecasting algorithms can lead to a better-than-chance forecasting performance. However, significance and better-than-chance are each typically evaluated against only a single null hypothesis, for example, that forecasts are generated by a Poisson process. We here argue that this should be considered only a first step. Our objective is to demonstrate the importance of testing complementary null hypotheses that represent alternative chance models. To ensure controlled conditions, we use synthetic data generated from simple mathematical models. Samples drawn from gamma distributions are used to generate sequences of random seizure times and random forecasts. We then determine the strength of cycles as a function of the cycle duration and calculate the sensitivity and fraction of time under alarm obtained for the random forecasting algorithm. In both analyses, we apply numerical, surrogate-based null-hypothesis testing methods. In the latter case, this includes a straightforward approach to correcting for multiple testing on nonindependent data. Counterintuitively, the random seizure-time sequences contain multiple prominent cycles, which are judged highly significant by the Rayleigh test. Moreover, randomly forecasting random seizure times results in a sensitivity of 79% at a fraction of time under alarm of only 42%, clearly outperforming a Poisson-like predictor. In both cases, however, the flexibility and versatility of surrogate-based null-hypothesis tests allow us to successfully reveal that all results can be explained by chance models. Before reaching conclusions on real cycles in epilepsy, the forecastability of seizures, and genuine capacity of forecasting algorithms, it is essential to test and reject several complementary null hypotheses. Many conclusions might not withstand such rigorous tests, allowing the community to focus on those that do.

Functional ultrasound localization micro- scopy (fULM) enables brain-wide mapping of neural activity at micron-scale resolution but suffers from limited sensitivity due to sparse and noisy microbubble (MB) detections. Extending fULM into three dimensions (3D) further exacerbates these challenges because of low-frequency matrix arrays, reduced localization efficiency, and severe data sparsity. To address these limitations, we developed a statistical framework that models MB arrivals in 3D as a Poisson process accounting for localization efficiency, detection probability, and backscattered amplitude. This analysis predicts that integrating amplitude with count-based fULM improves functional sensitivity, particularly under high MB concentrations where localization saturates. Three-dimensional MB advection simulations confirmed these predictions, showing that backscattering fULM (B-fULM) maintains sensitivity at higher MB concentrations where conventional fULM fails. In rat brain experiments, B-fULM yielded stronger and more robust stimulus-evoked responses, with SNR gains of 18% in the somatosensory cortex and 61% in the thalamus, while preserving super-resolved spatial detail ( $33.4~\mu $ m for B-fULM vs $35.7~\mu $ m for fULM). These results establish B-fULM as a practical and sensitive approach for super-resolved 3D functional neuroimaging.

Vaccination sites face the operational decision of determining the timing for notifying standby recipients (“jumpers”) to claim doses that would otherwise expire. Such timing decisions arise broadly in health-security operations involving perishable medical resources and responses to emerging health threats. This study formulates and analyzes a simulation-based model to evaluate notification policies within a framework defined by dose supply and site throughput levels. The notification policy is represented as a threshold based on the fraction of a dose’s remaining shelf life at which a jumper is alerted, and policy performance is measured using an objective function defined as the sum of average dose wait time and average requester wait time. We develop a sample-average approximation procedure to obtain performance bounds and optimality gaps, and subsequently relax key baseline assumptions through robustness analyses that examine time-varying requester arrivals modeled as a nonhomogeneous Poisson process, alternative jumper travel-time distributions, pooled jumper configurations, and alternative value weights capturing equity-efficiency preferences. Across the baseline and extended analyses, notification timing and system performance exhibit a nonmonotonic relationship. When supply is scarce, system performance varies little across notification thresholds, with later notification offering practical protection of priority access. Under balanced supply and demand, notifications near midshelf life typically perform well. When supply is abundant, higher-throughput sites benefit from earlier notification to reduce the risk of expiration. In many scenarios, a range of policies yields statistically indistinguishable performance, indicating robust near-best policies. The study provides a health decision analysis framework to help vaccination sites select notification thresholds tailored to their supply conditions and operational capacity, offering practical guidance for balancing equitable access with the efficient use of expiring healthcare resources.

Abstract We consider a perishable inventory system (PIS) in which demands for items arrive according to a Poisson process and items according to a renewal process. Stored items have a deterministic maximum lifetime ‘on the shelf.’ Exploiting a relation between the so-called virtual outdating time (VOT) process of this PIS and the workload process of the $$M/G/1+D$$ M / G / 1 + D queue, we prove a decomposition property of each of these two processes. Subsequently we analyze two generalizations of the above PIS, where the quality of items on the shelf is not constant. In the first one, there are two types of items, with different maximum lifetimes. In the second, the quality of an item gradually deteriorates with age.

Statistical methods for dynamic network analysis play an essential role in modelling the temporal dynamics of network structures. While many studies have modelled longitudinal networks based on continuous-time observations, research based on discrete-time observations remains relatively limited. This study introduces a statistical method that integrates dynamic stochastic block models with Poisson processes to analyse recurrent dyadic interaction events observed at discrete time points. A variational expectation-maximisation algorithm is employed for parameter estimation. The asymptotic properties of the proposed dynamic model are discussed. Simulation studies studies and real-world network applications demonstrate the effectiveness of the proposed model in modelling the temporal evolution of network structures and interaction patterns.

Know Today, Know Tomorrow: Ensemble Nowcasting of Bear Encounter Risk from Sighting Time Series.

This paper studies valuation under usage-timing uncertainty for random-time-use goods, defined as goods for which usage opportunities arrive at stochastic times. We model usage opportunities as a nonhomogeneous Poisson process and derive closed-form expressions for the expected present value of utility under constant, exponential, power-law, and oscillatory arrival rates. For oscillatory usage patterns, we show that the interaction between cycle frequency and discounting yields a phase-dependent ranking of feasible start dates, a phase-alignment premium, and a measure of the dollar-valued gain from switching between feasible start dates. An empirical application to backup-generator valuation demonstrates how observed power-interruption patterns translate into present-value upper bounds on the ownership costs a rational household should be willing to bear. The framework isolates demand-side usage-timing uncertainty, a dimension complementary to the supply-side deterioration and replacement problems emphasised in durable-goods models, and provides tools for acquisition, rental, and stockpiling decisions across household, business, and policy contexts.

Unmanned aerial vehicles (UAVs), with their rapid and flexible deployment capabilities, have emerged as an effective solution for providing emergency wireless connectivity in scenarios where traditional ground base stations (GBSs) cannot offer reliable communication links. To address the weak coverage experienced by cell-edge users associated with a GBS, this paper investigates a UAV-assisted surround-enhancement coverage strategy. In the proposed approach, the original cell is partitioned into two service regions, where the GBS and UAV individually support users within their designated coverage areas. To improve spectrum utilization efficiency, we analyze the mutual interference between the UAV and GBS under a spectrum-sharing framework. Meanwhile, the user distribution within the cell is modeled as a homogeneous Poisson point process, and both the GBS and UAV randomly allocate channels to their associated users. Analytical results demonstrate that the UAV-assisted scheme exhibits an optimal surround radius and flight altitude, and that a reasonable division of coverage regions between the GBS and UAV can fully leverage their respective coverage capabilities.

Polyvinyl alcohol (PVA), a widely used synthetic polymer, is known to effectively promote ice nucleation, but the underlying microscopic mechanism has long been controversial. On the basis of experimental evidence that PVA forms nanoscale aggregates in aqueous solution, we propose that its ice nucleation activity originates from heterogeneous nucleation on the surfaces of these aggregates. To validate this hypothesis, we performed large-scale molecular dynamics simulations using two idealized surface models representing the hydrophobic carbon backbone and the hydrophilic hydroxyl group surface of PVA aggregates. Our simulations demonstrate that the hydrophobic surface exhibits potent ice nucleation activity via a heterogeneous mechanism, whereas the hydrophilic surface shows a negligible effect on nucleation. To elucidate the physical mechanism, we employed a theoretical framework combining classical nucleation theory with a non-homogeneous Poisson process model. The analysis revealed that the hydrophobic surface promotes nucleation by substantially lowering the thermodynamic nucleation free energy barrier, an effect that overwhelms the concurrent slowing of interfacial water dynamics. Microstructural analysis further revealed that the hydrophobic surface induces the formation of an ordered, ice-like 6-membered ring structure in the interfacial water layer prior to the nucleation. This pre-ordered interfacial water layer serves as a template for ice crystal growth while also leading to slowed interfacial dynamics. This work provides a molecular explanation for the ice nucleation activity of PVA and highlights the critical role of polymer surface hydrophobicity and interfacial water structuring in heterogeneous ice nucleation.

Abstract Introduction College students frequently report insufficient sleep, but the extent to which structural schedule constraints alone -independent of individual behavior- limit sleep opportunity is not well quantified. In this study, we developed a computational simulation model to estimate how academic schedules, evening obligations, and weekend variability shape the maximum achievable sleep window in a synthetic student population. Methods We constructed a Monte Carlo agent-based model generating 10,000 synthetic weekly schedules based on distributions of publicly available university class times. Morning constraints were drawn from a normal distribution centered at 9:30 (SD=1.2 h). Evening constraints (labs, extracurriculars) were sampled from empirical distributions with a 30% probability of extending past 20:00. Study blocks were assigned using a Poisson process (λ=1.8/day). Sleep opportunity was defined as the longest continuous interval between the day’s final constraint (plus a 45-min wind-down buffer) and the next morning’s earliest constraint (minus a 45-min preparation buffer). Weekend days removed academic constraints but preserved social obligations with higher variance. Simulations were stratified into STEM–like and non-STEM–like schedules based on evening course likelihood. Results Across all schedules, the mean weekday sleep opportunity was 6.41 ± 1.05 hours, compared to 8.12 ± 1.32 hours on weekends (p < .001). Only 14.7% of weekday nights allowed ≥8 hours of potential sleep. STEM-modeled schedules produced 22.9% fewer nights with ≥8 hours opportunity than non-STEM schedules (12.1% vs. 15.7%). Schedules containing evening labs delayed modeled bedtime by 1.08 hours, reducing sleep opportunity by 0.74 hours per affected day. The highest restriction occurred in students with both early-morning classes and ≥2 evening constraints, yielding an average weekday opportunity of 5.38 hours. Conclusion Structural features of typical college schedules substantially restrict sleep opportunity even before accounting for student behavior. These simulations show that many students may be potentially chronically limited by schedule architecture alone, suggesting a need for academic policy reforms. Computational modeling provides a scalable method for assessing population-level determinants of sleep health without requiring human-subjects data. Support (if any)

This study seeks to advance the theoretical understanding and analytical framework of reflected backward stochastic differential equations (RBSDEs), providing new perspectives. Unlike traditional studies that primarily rely on standard Brownian motion and Poisson processes to model stochastic dynamics, our approach innovatively incorporates stochastic Jacod parameters into the formulation of the RBSDEs. By doing so, we are able to capture a broader class of stochastic behaviors and derive more robust and generalizable results. In particular, we begin by developing a rigorous a priori estimate, which serves as a foundational tool for subsequent analysis. Building on this estimate, we rigorously prove the existence and uniqueness of solutions in settings where the generator function includes jump components, thereby addressing complexities introduced by discontinuities in RBSDEs. This study differentiates itself from previous research that analyzed analogous RBSDE issues under more stringent conditions, generally incorporating a one-dimensional Brownian motion alongside an independent Poisson process to influence the price dynamics. Our study extends the theoretical scope of RBSDEs and provides a framework that can be applied to more complex stochastic systems, including those with multidimensional uncertainties and jump discontinuities, offering potential applications in advanced financial modeling, risk management, and related areas where stochastic dynamics with jumps play a critical role.