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Yucheng Pan

Publications and source records attributed to Yucheng Pan.

3 recordsLinked to original sources

Pointwise Convergence of Schr\"{o}dinger Operators in Bessel Potential Spaces

We study the pointwise convergence of solutions to the free Schr\"{o}dinger equation with initial data in the Bessel potential spaces $L_s^p(\mathbb{R}^n)$. We establish new sufficient regularity indices for pointwise convergence across the full range $1 \leq p < \infty$, and demonstrate via counterexamples that these indices are sharp for all $1 \leq p \leq 2$ in one dimension, as well as for $p=1$ or $p$ large enough in higher dimensions. The proofs rely on the high-dimensional stationary phase method.

math.AP

WILD-SAM: Phase-Aware Expert Adaptation of SAM for Landslide Detection in Wrapped InSAR Interferograms

Detecting slow-moving landslides directly from wrapped Interferometric Synthetic Aperture Radar (InSAR) interferograms is crucial for efficient geohazard monitoring, yet it remains fundamentally challenged by severe phase ambiguity and complex coherence noise. While the Segment Anything Model (SAM) offers a powerful foundation for segmentation, its direct transfer to wrapped phase data is hindered by a profound spectral domain shift, which suppresses the high-frequency fringes essential for boundary delineation. To bridge this gap, we propose WILD-SAM, a novel parameter-efficient fine-tuning framework specifically designed to adapt SAM for high-precision landslide detection on wrapped interferograms. Specifically, the architecture integrates a Phase-Aware Mixture-of-Experts (PA-MoE) Adapter into the frozen encoder to align spectral distributions and introduces a Wavelet-Guided Subband Enhancement (WGSE) strategy to generate frequency-aware dense prompts. The PA-MoE Adapter exploits a dynamic routing mechanism across heterogeneous convolutional experts to adaptively aggregate multi-scale spectral-textural priors, effectively aligning the distribution discrepancy between natural images and interferometric phase data. Meanwhile, the WGSE strategy leverages discrete wavelet transforms to explicitly disentangle high-frequency subbands and refine directional phase textures, injecting these structural cues as dense prompts to ensure topological integrity along sharp landslide boundaries. Extensive experiments on the ISSLIDE and ISSLIDE+ benchmarks demonstrate that WILD-SAM achieves state-of-the-art performance, significantly outperforming existing methods in both target completeness and contour fidelity.

cs.CV

On the rate of convergence for Landau type Schr\"odinger Operators

We study the pointwise convergence of Landau type Schr\"odinger operators within the fractional Sobolev space $W^{s,p}(\mathbb R)$. Our results extend those established by Bailey (Rev. Mat. Iberoam., 29 (2): 531-546, 2013) and Yuan, Zhao and Zheng (Nonlinear Anal., 208: Paper No. 112312, 28, 2021). Furthermore, we also analyze the convergence rate of Landau type Schr\"odinger operators along curves and derive a sharp result for the case of convergence along vertical lines.

math.AP