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Shengyu Tang

Publications and source records attributed to Shengyu Tang.

9 recordsLinked to original sources
arXiv2026

$L_p$ Brunn-Minkowski inequality for weighted dual quermassintegrals

We investigate the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals in weighted measure spaces, which is a special class of rotationally invariant measures proposed by Cordero-Erausquin and Rotem [Ann. Probab., {\bf 51} (2023)]. Specifically, the weighted dual quermassintegral is defined by integrating the radial density $|x|^{q-n}\phi(|x|)$ for $q\in(0,n]$, where $\phi$ is a positive radially non-increasing weight, it recovers the classical dual quermassintegral when $\phi\equiv1$. For $p\geq1$, we prove the $L_p$ Brunn-Minkowski inequality with concavity exponent $p/q$ under the condition that $t\mapsto\log\phi(e^t)$ is concave, which is exactly the natural convexity condition from Cordero-Erausquin and Rotem's paper in general, improving the exponent $1/n$ when $p=1$. For $p\in(0,1)$, we obtain the result with exponent $p/q$ under more strictly weight assumptions, together with explicit lower bounds for the admissible range of $p$.

math.MG↗
arXiv2026

$L_p$ Minkowski problem and Brunn-Minkowski inequality for dual quermassintegrals

This paper studies the core problems in the $L_p$ dual Brunn-Minkowski theory, encompassing the $L_p$ Minkowski problem and $L_p$ Brunn-Minkowski inequality for dual quermassintegrals. For the case $0<p<q\leq n$, we establish $C^0$ estimates for the $L_p$ dual Minkowski problem without symmetric assumptions, thereby resolving a related problem proposed by B\"or\"oczky-Chen-Liu-Saroglou in the smooth sense. We further prove the uniqueness of smooth solutions under appropriate conditions, provided the density function is sufficiently close to a constant in the H\"older norm. Finally, exploiting the fact that the uniqueness of the Minkowski type problem is equivalent to the validity of the Brunn-Minkowski inequality in a certain sense, we study the $L_p$ Brunn-Minkowski inequality for dual quermassintegrals for origin-symmetric convex bodies with $p<q$.

math.AP↗
arXiv2025

DMSORT: An efficient parallel maritime multi-object tracking architecture for unmanned vessel platforms

Accurate perception of the marine environment through robust multi-object tracking (MOT) is essential for ensuring safe vessel navigation and effective maritime surveillance. However, the complicated maritime environment often causes camera motion and subsequent visual degradation, posing significant challenges to MOT. To address this challenge, we propose an efficient Dual-branch Maritime SORT (DMSORT) method for maritime MOT. The core of the framework is a parallel tracker with affine compensation, which incorporates an object detection and re-identification (ReID) branch, along with a dedicated branch for dynamic camera motion estimation. Specifically, a Reversible Columnar Detection Network (RCDN) is integrated into the detection module to leverage multi-level visual features for robust object detection. Furthermore, a lightweight Transformer-based appearance extractor (Li-TAE) is designed to capture global contextual information and generate robust appearance features. Another branch decouples platform-induced and target-intrinsic motion by constructing a projective transformation, applying platform-motion compensation within the Kalman filter, and thereby stabilizing true object trajectories. Finally, a clustering-optimized feature fusion module effectively combines motion and appearance cues to ensure identity consistency under noise, occlusion, and drift. Extensive evaluations on the Singapore Maritime Dataset demonstrate that DMSORT achieves state-of-the-art performance. Notably, DMSORT attains the fastest runtime among existing ReID-based MOT frameworks while maintaining high identity consistency and robustness to jitter and occlusion. Code is available at: https://github.com/BiscuitsLzy/DMSORT-An-efficient-parallel-maritime-multi-object-tracking-architecture-.

cs.CV↗
arXiv2025

Gr\"unbaum's inequality for Gaussian and convex probability measures

A celebrated result in convex geometry is Gr\"unbaum's inequality, which quantifies how much volume of a convex body can be cut off by a hyperplane passing through its barycenter. In this work, we establish a series of sharp Gr\"unbaum-type inequalities - with equality characterizations - for probability measures under certain concavity assumptions. As an application, we apply the renowned Ehrhard inequality and deduce an ``Ehrhard-Gr\"unbaum'' inequality for the Gaussian measure on $\mathbb{R}^n$, which improves upon the bound derived from its log-concavity. For $s$-concave Radon measures, our framework provides a simpler proof of known results and, more importantly, yields the previously missing equality characterization. This is achieved by gaining new insight into the equality case of their Brunn-Minkowski-type inequality. Moreover, we show that these ``$s$-Gr\"unbaum'' inequalities can hold only when $s > -1$. However, for convex measures on the real line, we prove Gr\"unbaum-type inequalities involving their cumulative distribution function.

math.FA↗
arXiv2025

Underwater object detection in sonar imagery with detection transformer and Zero-shot neural architecture search

Underwater object detection using sonar imagery has become a critical and rapidly evolving research domain within marine technology. However, sonar images are characterized by lower resolution and sparser features compared to optical images, which seriously degrades the performance of object detection.To address these challenges, we specifically propose a Detection Transformer (DETR) architecture optimized with a Neural Architecture Search (NAS) approach called NAS-DETR for object detection in sonar images. First, an improved Zero-shot Neural Architecture Search (NAS) method based on the maximum entropy principle is proposed to identify a real-time, high-representational-capacity CNN-Transformer backbone for sonar image detection. This method enables the efficient discovery of high-performance network architectures with low computational and time overhead. Subsequently, the backbone is combined with a Feature Pyramid Network (FPN) and a deformable attention-based Transformer decoder to construct a complete network architecture. This architecture integrates various advanced components and training schemes to enhance overall performance. Extensive experiments demonstrate that this architecture achieves state-of-the-art performance on two Representative datasets, while maintaining minimal overhead in real-time efficiency and computational complexity. Furthermore, correlation analysis between the key parameters and differential entropy-based fitness function is performed to enhance the interpretability of the proposed framework. To the best of our knowledge, this is the first work in the field of sonar object detection to integrate the DETR architecture with a NAS search mechanism.

cs.CV↗
arXiv2024

The Weighted $L^p$ Minkowski Problem

The Minkowski problem in convex geometry concerns showing that a given Borel measure on the unit sphere is, up to perhaps a constant, some type of surface area measure of a convex body. Two types of Minkowski problems in particular are an active area of research: $L^p$ Minkowski problems, introduced by Lutwak and (Lutwak, Yang, and Zhang), and weighted Minkowski problems, introduced by Livshyts. For the latter, the Gaussian Minkowski problem, whose primary investigators were (Huang, Xi and Zhao), is the most prevalent. In this work, we consider weighted surface area in the $L^p$ setting. We propose a framework going beyond the Gaussian setting by focusing on rotationally invariant measures, mirroring the recent development of the Gardner-Zvavitch inequality for rotationally invariant, log-concave measures. Our results include existence for all $p \in \mathbb R$ (with symmetry assumptions in certain instances). We also have uniqueness for $p \geq 1$ under a concavity assumption. Finally, we obtain results in the so-called "small mass regime" using degree theory, as instigated in the Gaussian case by (Huang, Xi and Zhao).

math.AP↗
arXiv2024

The Generalized Gaussian Minkowski Problem

This article delves into the $L_p$ Minkowski problem within the framework of generalized Gaussian probability space. This type of probability space was initially introduced in information theory through the seminal works of Lutwak, Yang, and Zhang [49,50], as well as by Lutwak, Lv, Yang, and Zhang [45]. The primary focus of this article lies in examining the existence of this problem. While the variational method is employed to explore the necessary and sufficient conditions for the existence of the normalized Minkowski problem when $p \in \mathbb{R} \setminus \{0\}$, our main emphasis is on the existence of the generalized Gaussian Minkowski problem without the normalization requirement, particularly in the smooth category for $p \geq 1$.

math.AP↗
arXiv2021

Effect of symmetry defect on the edge resonance of semi-infinite FGM plates

The effect of asymmetric functionally graded material on the edge resonance and the Fano resonance in semi-infinite FGM plates are reported in this work. The edge resonance is weakened by the material perturbation and the complete mode conversion is illustrated with incident $S_0$ mode. The Fano resonance occurs on the reflected $A_0$ mode as a result of interference between the resonance and direct scattering with incident $A_0$ mode. A hybrid analytical model based on the collocation discretization and the modal decomposition of the elastic field is developed to analyze the scattering properties of the semi-infinite plates. The Fano line-shape is discussed in detail. The results show that the Fano line shape is sensitive to the volume fraction, which is beneficial for the quantitative guided wave application.

physics.class-ph↗