arXiv subjects

Qingshan Yang

Publications and source records attributed to Qingshan Yang.

6 recordsLinked to original sources

arXiv2026

Small ball probabilities and Chung's law of the iterated logarithm for Gaussian Volterra processes with power-type kernels

Consider the Gaussian Volterra process introduced by Mishura and Shklyar \cite{MS22a,MS22b}, $$ X(t) = \int_0^t r^\alpha \left( \int_r^t u^\beta (u-r)^\gamma\,du \right)dW_r, \qquad t\ge 0, $$ where $$ \alpha>-\frac12, \quad \gamma\in\left(-1,-\frac12\right), \quad H:=\alpha+\beta+\gamma+\frac32>0. $$ We obtain two-sided estimates for the small ball probabilities of $X$. As applications, we prove Chung's laws of the iterated logarithm (Chung's LILs) at every fixed point $t>0$, at the origin, and at infinity. The fixed-time result follows from the small ball estimates and the Lamperti transformation, whereas the results at the origin and infinity follow from Talagrand's lower-class criteria \cite{talagrand1996lower}. These results show that $\gamma+\frac32$ determines the local roughness and the small ball exponent, $\alpha+\beta$ determines the scale of local fluctuations at fixed positive times, and $H$ governs the self-similar scaling at the origin and infinity.

math.PR↗

arXiv2026

Method for 3D printing of cubic microbubbles: fully enclosed thin-walled microcavities with ultra-high aspect ratios

A microbubble is, in essence, a fully enclosed thin-walled microcavity. Unlike spherical microbubbles formed by expansions, 3D printing enables the free definition of their geometry, allowing precise control over shape and dimensions during fabrication. However, the geometric nature of microbubbles poses significant challenges for conventional photoresist-based lithographic microfabrication due to their fragile thin-walls, enclosed hollow volumes, and high sensitivity to mechanical stresses. These characteristics prevent developer solvents from accessing the internal cavities to remove unexposed photoresist. Two-photon polymerisation (2PP) is a laser-based 3D microprinting technique capable of sub-diffraction-limited resolution, offering exceptional design freedom for fabricating complex micro-architectures in photoresists. In this study, we demonstrate a 2PP-based method that overcomes these limitations and, for the first time, enables the successful fabrication of cubic microbubbles with ultra-high-aspect-ratio thin walls and fully enclosed microcavities using high-viscosity SU-8 2050 photoresist. The optimised process parameters and structural design facilitate efficient extraction of unexposed photoresist from the cavity interior while achieving a thin-wall ultra-high aspect ratio of approximately 340:1. The hollow nature and mechanical integrity of the printed structures were experimentally confirmed using micromanipulator-based probing. The proposed method maintains excellent dimensional accuracy and significantly reduces printing time for large-scale and high-count builds in 2PP processes. Such microbubbles are fundamental building blocks for optical resonators, microelectromechanical systems (MEMS) pressure sensors, microfluidic reaction chambers, and emerging metamaterials.

physics.optics↗

arXiv2025

S2R-Bench: A Sim-to-Real Evaluation Benchmark for Autonomous Driving

Safety is a long-standing and the final pursuit in the development of autonomous driving systems, with a significant portion of safety challenge arising from perception. How to effectively evaluate the safety as well as the reliability of perception algorithms is becoming an emerging issue. Despite its critical importance, existing perception methods exhibit a limitation in their robustness, primarily due to the use of benchmarks are entierly simulated, which fail to align predicted results with actual outcomes, particularly under extreme weather conditions and sensor anomalies that are prevalent in real-world scenarios. To fill this gap, in this study, we propose a Sim-to-Real Evaluation Benchmark for Autonomous Driving (S2R-Bench). We collect diverse sensor anomaly data under various road conditions to evaluate the robustness of autonomous driving perception methods in a comprehensive and realistic manner. This is the first corruption robustness benchmark based on real-world scenarios, encompassing various road conditions, weather conditions, lighting intensities, and time periods. By comparing real-world data with simulated data, we demonstrate the reliability and practical significance of the collected data for real-world applications. We hope that this dataset will advance future research and contribute to the development of more robust perception models for autonomous driving. This dataset is released on https://github.com/adept-thu/S2R-Bench.

cs.RO↗

arXiv2023

Dual Radar: A Multi-modal Dataset with Dual 4D Radar for Autonomous Driving

Radar has stronger adaptability in adverse scenarios for autonomous driving environmental perception compared to widely adopted cameras and LiDARs. Compared with commonly used 3D radars, the latest 4D radars have precise vertical resolution and higher point cloud density, making it a highly promising sensor for autonomous driving in complex environmental perception. However, due to the much higher noise than LiDAR, manufacturers choose different filtering strategies, resulting in an inverse ratio between noise level and point cloud density. There is still a lack of comparative analysis on which method is beneficial for deep learning-based perception algorithms in autonomous driving. One of the main reasons is that current datasets only adopt one type of 4D radar, making it difficult to compare different 4D radars in the same scene. Therefore, in this paper, we introduce a novel large-scale multi-modal dataset featuring, for the first time, two types of 4D radars captured simultaneously. This dataset enables further research into effective 4D radar perception algorithms.Our dataset consists of 151 consecutive series, most of which last 20 seconds and contain 10,007 meticulously synchronized and annotated frames. Moreover, our dataset captures a variety of challenging driving scenarios, including many road conditions, weather conditions, nighttime and daytime with different lighting intensities and periods. Our dataset annotates consecutive frames, which can be applied to 3D object detection and tracking, and also supports the study of multi-modal tasks. We experimentally validate our dataset, providing valuable results for studying different types of 4D radars. This dataset is released on https://github.com/adept-thu/Dual-Radar.

cs.CV↗

arXiv2022

Functional large deviations for Stroock's approximation to a class of Gaussian processes with application to small noise diffusions

Letting~$N=\left\{N(t), t\geq0\right\}$ be a standard Poisson process, Stroock~ \cite{Stroock-1981} constructed a family of continuous processes by $$Θ_ε(t)=\int_0^tθ_ε(r)dr, \ \ \ \ \ 0 \le t \le 1,$$ where $θ_ε(r)=\frac{1}ε(-1)^{N(ε^{-2}r)}$, and proved that it weakly converges to a standard Brownian motion under the continuous function topology. We establish the functional large deviations principle (LDP) for the approximations of a class of Gaussian processes constructed by integrals over $Θ_ε(t)$, and find the explicit form for rate function. As an application, we consider the following (non-Markovian) stochastic differential equation \begin{equation*} \begin{aligned} X^ε(t) &=x_{0}+\int^{t}_{0}b(X^ε(s))ds+λ(ε)\int^{t}_{0}σ(X^ε(s))dΘ_ε(s), \end{aligned} \end{equation*} where $b$ and $σ$ are both Lipschitz functions, and establish its Freidlin-Wentzell type LDP as $ε\rightarrow 0$. The rate function indicates a phase transition phenomenon as $λ(ε)$ moves from one region to the other.

math.PR↗

arXiv2015

The Hitting Times of A Stochastic Epidemic Model

In this paper, we focus on the hitting times of a stochastic epidemic model presented by \cite{Gray}. Under the help of the auxiliary stopping times, we investigate the asymptotic limits of the hitting times by the variations of calculus and the large deviation inequalities when the noise is sufficiently small. It can be shown that the relative position between the initial state and the hitting state determines the scope of the hitting times greatly.

math.PR↗