arXiv subjects

Rui Bai

Publications and source records attributed to Rui Bai.

8 recordsLinked to original sources

arXiv2026

Exponential Mixing for 2D Stochastic Damped Euler Equation Driven by Bounded Noise

In this paper, we study the long-time behaviour of the two-dimensional stochastic damped Euler equation on the torus driven by bounded random forcing. Unlike stochastic Navier-Stokes or fractionally dissipative Euler equations, the model possesses no viscous regularisation, so the classical parabolic smoothing is unavailable. We prove that when the damping coefficient is sufficiently large, the associated Markov semigroup admits a unique invariant measure and converges exponentially fast to equilibrium. The key ingredient is the establishment of a global-in-time $W^{1,\infty}$ estimate for the vorticity. This estimate yields a compact absorbing mechanism in $C(\mathbb{T}^2)$, which enables us to establish the uniqueness of the invariant measure and exponential mixing. To the best of our knowledge, this is the first exponential mixing result for a genuinely inviscid stochastic Euler-type equation. Our approach demonstrates that sufficiently strong linear damping can effectively replace the compactness mechanism usually provided by viscosity and is expected to be applicable to other inviscid or weakly dissipative stochastic partial differential equations driven by bounded random forcing.

math.PR↗

arXiv2025

Large deviations for invariant measure of stochastic Allen-Cahn equation with inhomogeneous boundary conditions and multiplicative noise

We establish a small-noise large deviation principle for the family of invariant measures $\{\mu_\epsilon\}_{\epsilon>0}$ associated with the one-dimensional stochastic Allen-Cahn equation, subject to inhomogeneous Dirichlet boundary conditions and driven by unbounded multiplicative noise. The main novelty is that the deterministic system is only weakly dissipative, while the noise coefficient is allowed to have strictly sublinear growth arbitrarily close to linear. Using L. Simon's convergence theorem, we prove that every trajectory of the corresponding noiseless equation converges, as time tends to infinity, to the unique minimiser of the Ginzburg-Landau energy functional determined by the boundary conditions. A key ingredient is an exponential estimate for the invariant measures outside bounded subsets of $W^{k^\star,p^\star}$, where $k^\star p^\star>1$ and $p^\star$ are sufficiently large; such subsets are compact in the underlying space of continuous functions. As a consequence of the large deviation principle, we show that, as $\epsilon\to 0$, the invariant measures $\mu_\epsilon$ concentrate exponentially fast around the unique minimiser.

math.PR↗

arXiv2025

Artificial Intelligence-derived Cardiotocography Age as a Digital Biomarker for Predicting Future Adverse Pregnancy Outcomes

Cardiotocography (CTG) is a low-cost, non-invasive fetal health assessment technique used globally, especially in underdeveloped countries. However, it is currently mainly used to identify the fetus's current status (e.g., fetal acidosis or hypoxia), and the potential of CTG in predicting future adverse pregnancy outcomes has not been fully explored. We aim to develop an AI-based model that predicts biological age from CTG time series (named CTGage), then calculate the age gap between CTGage and actual age (named CTGage-gap), and use this gap as a new digital biomarker for future adverse pregnancy outcomes. The CTGage model is developed using 61,140 records from 11,385 pregnant women, collected at Peking University People's Hospital between 2018 and 2022. For model training, a structurally designed 1D convolutional neural network is used, incorporating distribution-aligned augmented regression technology. The CTGage-gap is categorized into five groups: < -21 days (underestimation group), -21 to -7 days, -7 to 7 days (normal group), 7 to 21 days, and > 21 days (overestimation group). We further defined the underestimation group and overestimation group together as the high-risk group. We then compare the incidence of adverse outcomes and maternal diseases across these groups. The average absolute error of the CTGage model is 10.91 days. When comparing the overestimation group with the normal group, premature infants incidence is 5.33% vs. 1.42% (p < 0.05) and gestational diabetes mellitus (GDM) incidence is 31.93% vs. 20.86% (p < 0.05). When comparing the underestimation group with the normal group, low birth weight incidence is 0.17% vs. 0.15% (p < 0.05) and anaemia incidence is 37.51% vs. 34.74% (p < 0.05). Artificial intelligence-derived CTGage can predict the future risk of adverse pregnancy outcomes and hold potential as a novel, non-invasive, and easily accessible digital biomarker.

eess.SP↗

arXiv2025

Safe and Efficient Lane-Changing for Autonomous Vehicles: An Improved Double Quintic Polynomial Approach with Time-to-Collision Evaluation

Autonomous driving technology has made significant advancements in recent years, yet challenges remain in ensuring safe and comfortable interactions with human-driven vehicles (HDVs), particularly during lane-changing maneuvers. This paper proposes an improved double quintic polynomial approach for safe and efficient lane-changing in mixed traffic environments. The proposed method integrates a time-to-collision (TTC) based evaluation mechanism directly into the trajectory optimization process, ensuring that the ego vehicle proactively maintains a safe gap from surrounding HDVs throughout the maneuver. The framework comprises state estimation for both the autonomous vehicle (AV) and HDVs, trajectory generation using double quintic polynomials, real-time TTC computation, and adaptive trajectory evaluation. To the best of our knowledge, this is the first work to embed an analytic TTC penalty directly into the closed-form double-quintic polynomial solver, enabling real-time safety-aware trajectory generation without post-hoc validation. Extensive simulations conducted under diverse traffic scenarios demonstrate the safety, efficiency, and comfort of the proposed approach compared to conventional methods such as quintic polynomials, Bezier curves, and B-splines. The results highlight that the improved method not only avoids collisions but also ensures smooth transitions and adaptive decision-making in dynamic environments. This work bridges the gap between model-based and adaptive trajectory planning approaches, offering a stable solution for real-world autonomous driving applications.

cs.RO↗

arXiv2025

Simultaneous Polysomnography and Cardiotocography Reveal Temporal Correlation Between Maternal Obstructive Sleep Apnea and Fetal Hypoxia

Background: Obstructive sleep apnea syndrome (OSAS) during pregnancy is common and can negatively affect fetal outcomes. However, studies on the immediate effects of maternal hypoxia on fetal heart rate (FHR) changes are lacking. Methods: We used time-synchronized polysomnography (PSG) and cardiotocography (CTG) data from two cohorts to analyze the correlation between maternal hypoxia and FHR changes (accelerations or decelerations). Maternal hypoxic event characteristics were analyzed using generalized linear modeling (GLM) to assess their associations with different FHR changes. Results: A total of 118 pregnant women participated. FHR changes were significantly associated with maternal hypoxia, primarily characterized by accelerations. A longer hypoxic duration correlated with more significant FHR accelerations (P < 0.05), while prolonged hypoxia and greater SpO2 drop were linked to FHR decelerations (P < 0.05). Both cohorts showed a transient increase in FHR during maternal hypoxia, which returned to baseline after the event resolved. Conclusion: Maternal hypoxia significantly affects FHR, suggesting that maternal OSAS may contribute to fetal hypoxia. These findings highlight the importance of maternal-fetal interactions and provide insights for future interventions.

eess.SP↗

arXiv2024

CEHA: A Dataset of Conflict Events in the Horn of Africa

Natural Language Processing (NLP) of news articles can play an important role in understanding the dynamics and causes of violent conflict. Despite the availability of datasets categorizing various conflict events, the existing labels often do not cover all of the fine-grained violent conflict event types relevant to areas like the Horn of Africa. In this paper, we introduce a new benchmark dataset Conflict Events in the Horn of Africa region (CEHA) and propose a new task for identifying violent conflict events using online resources with this dataset. The dataset consists of 500 English event descriptions regarding conflict events in the Horn of Africa region with fine-grained event-type definitions that emphasize the cause of the conflict. This dataset categorizes the key types of conflict risk according to specific areas required by stakeholders in the Humanitarian-Peace-Development Nexus. Additionally, we conduct extensive experiments on two tasks supported by this dataset: Event-relevance Classification and Event-type Classification. Our baseline models demonstrate the challenging nature of these tasks and the usefulness of our dataset for model evaluations in low-resource settings with limited number of training data.

cs.CL↗

arXiv2024

Large deviations principle for invariant measures of stochastic Burgers equations

We study the small noise asymptotic for stochastic Burgers equations on $(0,1)$ with Dirichlet boundary condition. We consider the case that the noise is more singular than space-time white noise. We let the noise magnitude $\sqrt{\epsilon} \rightarrow 0$ and the covariance operator $Q_\epsilon$ is convergent to $(-\Delta)^{\frac 1 2}$ and prove a large deviations principle for solutions, uniformly with respect to the initial value of equation. Furthermore, we set $Q_\epsilon$ to be a trace class operator and converge to $(-\Delta)^{\frac{\alpha}{2}}$ with $\alpha<1$ in a suitable way such that the invariant measures exist. Then, we prove the large deviations principle for the invariant measures of stochastic Burgers equations.

math.PR↗

arXiv2023

Make Your Decision Convincing! A Unified Two-Stage Framework: Self-Attribution and Decision-Making

Explaining black-box model behavior with natural language has achieved impressive results in various NLP tasks. Recent research has explored the utilization of subsequences from the input text as a rationale, providing users with evidence to support the model decision. Although existing frameworks excel in generating high-quality rationales while achieving high task performance, they neglect to account for the unreliable link between the generated rationale and model decision. In simpler terms, a model may make correct decisions while attributing wrong rationales, or make poor decisions while attributing correct rationales. To mitigate this issue, we propose a unified two-stage framework known as Self-Attribution and Decision-Making (SADM). Through extensive experiments on five reasoning datasets from the ERASER benchmark, we demonstrate that our framework not only establishes a more reliable link between the generated rationale and model decision but also achieves competitive results in task performance and the quality of rationale. Furthermore, we explore the potential of our framework in semi-supervised scenarios.

cs.CL↗