arXiv subjects

Xinyi Liang

Publications and source records attributed to Xinyi Liang.

3 recordsLinked to original sources

arXiv2026

A Counterexample to a Conjecture of Liu and Qian and a Refined Inverse Theorem for Restricted Sumsets in $\mathbb{Z}_p$

Let $p$ be a prime and let $A,B$ be nonempty subsets of the cyclic group $\mathbb{Z}_p$ with $|A|\neq |B|$. The Alon--Nathanson--Ruzsa theorem gives the lower bound \[ |A\rplus B|\ge \min\{p,\,|A|+|B|-2\}, \] where $A\rplus B=\{a+b:a\in A,\ b\in B,\ a\neq b\}$ is the restricted sumset. The inverse problem of characterizing all critical pairs $(A,B)$ attaining equality was posed by Alon, Nathanson, and Ruzsa in 1996 and remains open. Recently, Liu and Qian solved the inverse problem under the assumption that at least one of the sets is an arithmetic progression, and proposed a conjecture for the general case. In this paper, we first exhibit a counterexample to their conjecture, which arises in the boundary case $|A|+|B|=p$. This counterexample shows that the original conjecture is false without additional restrictions. Motivated by this, we formulate and prove a refined inverse theorem under the natural hypothesis $|A|+|B|\le p-1$. Our proof relies on the results of Liu and Qian together with a new counting argument.

math.NT↗

arXiv2026

Enhanced Emittance Evaluation using 2D Transverse Phase Space Distributions, High Resolution Image Denoising, and Deep Learning

Next-generation particle accelerators demand advanced beam-diagnostic capabilities to ensure high performance, operational reliability, and sustainable machine operation. Increasing beam intensities and stored energies make the precise characterization of transverse profiles, phase-space distributions, and halos often five orders of magnitude below the core but with significant environmental impact essential for loss mitigation and machine protection. Traditional analysis methods struggle with the heterogeneous, noisy, and non-Gaussian data produced under realistic operating conditions. This work presents a novel tool based on an unsupervised deep-convolutional neural-network framework that significantly enhances image denoising and restoration for emittance measurements. The method reconstructs beam-halo structures with unprecedented resolution, detecting signals at radii beyond seven standard deviations and particle densities below 10 -4 of the total beam intensity. Despite very low signal-to-noise ratios and small, non-annotated datasets, the approach preserves fine structures and reveals halo features previously unobserved at pilot installations. Built on a U-Net architecture with tailored early-stopping strategies and physics-informed metrics, the framework operates entirely on CPUs and requires minimal computational resources. The results demonstrate the potential of unsupervised deep learning as an enabling technology for high-dynamic-range beam diagnostics and motivate further development of systematic benchmarking and physics-informed learning strategies.

physics.acc-ph↗

arXiv2026

High-Resolution Image Reconstruction with Unsupervised Learning and Noisy Data Applied to Ion-Beam Dynamics for Particle Accelerators

Image reconstruction in the presence of severe degradation remains a challenging inverse problem, particularly in beam diagnostics for high-energy physics accelerators. As modern facilities demand precise detection of beam halo structures to control losses, traditional analysis tools have reached their performance limits. This work reviews existing image-processing techniques for data cleaning, contour extraction, and emittance reconstruction, and introduces a novel approach based on convolutional filtering and neural networks with optimized early-stopping strategies in order to control overfitting. Despite the absence of training datasets, the proposed unsupervised framework achieves robust denoising and high-fidelity reconstruction of beam emittance images under low signal-to-noise conditions. The method extends measurable amplitudes beyond seven standard deviations, enabling unprecedented halo resolution.

cs.CV↗