arXiv subjects

Yuanlin Li

Publications and source records attributed to Yuanlin Li.

At least 19 recordsLinked to original sources

arXiv2026

Artificial Anisotropy Induced Bound States in the Continuum for Integrated Photonic Waveguide

Bound states in the continuum (BICs) enable counterintuitive light confinement without radiation loss, providing a powerful foundation for integrated photonic waveguides. However, existing BIC waveguides are predominantly realized through geometry-dependent designs, where the BIC condition is restricted to narrowly defined structural parameters, limiting design flexibility and practical applicability. Artificial optical anisotropy is introduced as a new design paradigm for BIC waveguides. Implemented using subwavelength-grating (SWG) metamaterials, continuously tailorable anisotropy provides an independent degree of freedom for deterministically reshaping the radiative continuum, enabling flexible formation and systematic control of BIC waveguides over a broad design space. Anisotropy-engineered symmetry breaking further enables controllable asymmetric radiation and precisely tailored field leakage. This paradigm transforms BIC waveguides from geometry-constrained structures into an anisotropy-engineered platform, establishing a general framework for programmable radiation engineering and next-generation integrated photonic devices.

physics.optics↗

arXiv2026

The equality between the Erd\H{o}s-Ginzburg-Ziv constant and the short product-one constant for finite nonabelian groups

Let $G$ be a finite group, and let $\exp(G)$ denote its exponent. The Erd\H{o}s-Ginzburg-Ziv constant $s(G)$ is the least integer forcing a product-one subsequence of length $\exp(G)$, while the short product-one constant $\eta(G)$ is the least integer forcing a nonempty product-one subsequence of length at most $\exp(G)$. The natural nonabelian extension of a conjecture [W. Gao, \emph{On zero-sum subsequences of restricted size II}, Discrete Math. 2003] on the Erd\H{o}s-Ginzburg-Ziv constant in finite abelian groups predicts that $s(G)=\eta(G)+\exp(G)-1.$ We confirm this equality for every finite nonabelian group $G$ having a cyclic subgroup of index $p$, where $p$ is the smallest prime divisor of $|G|$. As further consequences, we determine all generalized Erd\H{o}s-Ginzburg-Ziv constants $s_{m\exp(G)}(G)$ for this family of groups.

math.CO↗

arXiv2026

GraphMAR: Geometry-Aware Graph Learning Framework for Spatially Adaptive CT Metal Artifact Reduction

Computed tomography (CT) metal artifact reduction (MAR) aims to reduce the severe streaking artifacts induced by metallic implants and other high-density objects. Effective MAR generally requires both accurate artifact localization and artifact removal. Sinogram-domain methods can exploit explicit geometric cues, such as metal traces, to identify metal-corrupted measurements, while requiring raw projection data, which is often unavailable in clinical and practical scenarios. Image-domain methods are more flexible and widely applicable, yet they usually lack comparable geometric guidance, limiting their ability to localize artifacts and leading to suboptimal results. To address this limitation, we propose GraphMAR, a geometry-aware learning framework for explicit artifact identification and spatially adaptive MAR in the image domain. The key idea is to introduce graph-based geometric modeling as an image-domain analogue of sinogram metal traces. Specifically, we first construct a geometric graph from the metal mask and derive a geometric density graph that coarsely localizes artifact-prone regions according to inter-implant geometry. We then design GraphMoE, a graph-routed mixture-of-experts module that builds a polar-coordinate artifact graph in feature space and adaptively routes different experts to different spatial regions for MAR. By aligning the learned routing maps with the geometric density graph, GraphMAR provides explicit and interpretable artifact localization while enabling region-adaptive artifact reduction. Experiments on both simulated and real-world datasets demonstrate that GraphMAR achieves superior MAR performance compared with existing methods. To the best of our knowledge, this is the first work to introduce graph-based modeling for CT MAR and to enable explicit artifact identification in the image domain, improving both restoration quality and interpretability.

cs.CV↗

arXiv2025

Radiologist-in-the-Loop Self-Training for Generalizable CT Metal Artifact Reduction

Metal artifacts in computed tomography (CT) images can significantly degrade image quality and impede accurate diagnosis. Supervised metal artifact reduction (MAR) methods, trained using simulated datasets, often struggle to perform well on real clinical CT images due to a substantial domain gap. Although state-of-the-art semi-supervised methods use pseudo ground-truths generated by a prior network to mitigate this issue, their reliance on a fixed prior limits both the quality and quantity of these pseudo ground-truths, introducing confirmation bias and reducing clinical applicability. To address these limitations, we propose a novel Radiologist-In-the-loop SElf-training framework for MAR, termed RISE-MAR, which can integrate radiologists' feedback into the semi-supervised learning process, progressively improving the quality and quantity of pseudo ground-truths for enhanced generalization on real clinical CT images. For quality assurance, we introduce a clinical quality assessor model that emulates radiologist evaluations, effectively selecting high-quality pseudo ground-truths for semi-supervised training. For quantity assurance, our self-training framework iteratively generates additional high-quality pseudo ground-truths, expanding the clinical dataset and further improving model generalization. Extensive experimental results on multiple clinical datasets demonstrate the superior generalization performance of our RISE-MAR over state-of-the-art methods, advancing the development of MAR models for practical application. Code is available at https://github.com/Masaaki-75/rise-mar.

eess.IV↗

arXiv2024

STS MICCAI 2023 Challenge: Grand challenge on 2D and 3D semi-supervised tooth segmentation

Computer-aided design (CAD) tools are increasingly popular in modern dental practice, particularly for treatment planning or comprehensive prognosis evaluation. In particular, the 2D panoramic X-ray image efficiently detects invisible caries, impacted teeth and supernumerary teeth in children, while the 3D dental cone beam computed tomography (CBCT) is widely used in orthodontics and endodontics due to its low radiation dose. However, there is no open-access 2D public dataset for children's teeth and no open 3D dental CBCT dataset, which limits the development of automatic algorithms for segmenting teeth and analyzing diseases. The Semi-supervised Teeth Segmentation (STS) Challenge, a pioneering event in tooth segmentation, was held as a part of the MICCAI 2023 ToothFairy Workshop on the Alibaba Tianchi platform. This challenge aims to investigate effective semi-supervised tooth segmentation algorithms to advance the field of dentistry. In this challenge, we provide two modalities including the 2D panoramic X-ray images and the 3D CBCT tooth volumes. In Task 1, the goal was to segment tooth regions in panoramic X-ray images of both adult and pediatric teeth. Task 2 involved segmenting tooth sections using CBCT volumes. Limited labelled images with mostly unlabelled ones were provided in this challenge prompt using semi-supervised algorithms for training. In the preliminary round, the challenge received registration and result submission by 434 teams, with 64 advancing to the final round. This paper summarizes the diverse methods employed by the top-ranking teams in the STS MICCAI 2023 Challenge.

cs.CV↗

arXiv2021

additive bases of abelian groups of rank 2

Let $G$ be a finite abelian group and $p$ be the smallest prime dividing $|G|$. Let $S$ be a sequence over $G$. We say that $S$ is regular if for every proper subgroup $H \subsetneq G$, $S$ contains at most $|H|-1$ terms from $H$. Let $\mathsf c_0(G)$ be the smallest integer $t$ such that every regular sequence $S$ over $G$ of length $|S|\geq t$ forms an additive basis of $G$, i.e., $\sum(S)=G$. The invariant $\mathsf c_0(G)$ was first studied by Olson and Peng in 1980's, and since then it has been determined for all finite abelian groups except for the groups with rank 2 and a few groups of rank 3 or 4 with order less than $10^8$. In this paper, we focus on the remaining case concerning groups of rank 2. It was conjectured by Gao et al. (Acta Arith. 168 (2015) 247-267) that $\mathsf c_0(G)=m(G)$. We confirm the conjecture for the case when $G=C_{n_1}\oplus C_{n_2}$ with $n_1|n_2$, $n_1\geq 2p$, $p\geq 3$ and $n_1n_2\geq 72p^6$.

math.CO↗

arXiv2021

Extremal product-one free sequences and $|G|$-product-one free sequences of a metacyclic group

Let $G$ be a multiplicatively written finite group. We denote by $\mathsf E(G)$ the smallest integer $t$ such that every sequence of $t$ elements in $G$ contains a product-one subsequence of length $|G|$. In 1961, Erdős, Ginzburg and Ziv proved that $\mathsf E(G)\leq 2|G|-1$ for every finite abelian group $G$ and this result is known as the Erdős-Ginzburg-Ziv Theorem. In 2005, Zhuang and Gao conjectured that $\mathsf E(G)=\mathsf d(G)+|G|$ for every finite group, where $\mathsf d(G)$ is the small Davenport constant. Very recently, we confirmed this conjecture for the case when $G=\langle x, y| x^p=y^m=1, x^{-1}yx=y^r\rangle$ where $p$ is the smallest prime divisor of $|G|$ and $\mbox{gcd}(p(r-1), m)=1$. In this paper, we study the associated inverse problems on $\mathsf d(G)$ and $\mathsf E(G)$. Our main results characterize the structure of any product-one free sequence with extremal length $\mathsf d(G)$, and that of any $|G|$-product-one free sequence with extremal length $\mathsf E(G)-1$.

math.CO↗

arXiv2021

On the invariant E(G) for groups of odd order

math.CO↗

arXiv2021

On a conjecture of Zhuang and Gao

math.CO↗

arXiv2021

Additive bases of $C_3\oplus C_{3q}$

Let $G$ be a finite abelian group and $p$ be the smallest prime dividing $|G|$. Let $S$ be a sequence over $G$. We say that $S$ is regular if for every proper subgroup $H \subsetneq G$, $S$ contains at most $|H|-1$ terms from $H$. Let $\mathsf c_0(G)$ be the smallest integer $t$ such that every regular sequence $S$ over $G$ of length $|S|\geq t$ forms an additive basis of $G$, i.e., $\sum(S)=G$. The invariant $\mathsf c_0(G)$ was first studied by Olson and Peng in 1980's, and since then it has been determined for all finite abelian groups except for the groups with rank 2 and a few groups of rank 3 or 4 with order less than $10^8$. In this paper, we focus on the remaining case concerning groups of rank 2. It was conjectured by the first author and Han (Int. J. Number Theory 13 (2017) 2453-2459) that $\mathsf c_0(G)=pn+2p-3$ where $G=C_p\oplus C_{pn}$ with $n\geq 3$. We confirm the conjecture for the case when $p=3$ and $n=q \,(\geq 5)$ is a prime number.

math.CO↗

arXiv2020

On clean, weakly clean, and feebly clean commutative group rings

A ring $R$ is said to be clean if each element of $R$ can be written as the sum of a unit and an idempotent. $R$ is said to be weakly clean if each element of $R$ is either a sum or a difference of a unit and an idempotent, and $R$ is said to be feebly clean if every element $r$ can be written as $r=u+e_1-e_2$, where $u$ is a unit and $e_1,e_2$ are orthogonal idempotents. Clearly clean rings are weakly clean rings and both of them are feebly clean. In a recent article (J. Algebra Appl. 17 (2018), 1850111(5 pages)), McGoven characterized when the group ring $\mathbb Z_{(p)}[C_q]$ is weakly clean and feebly clean, where $p, q$ are distinct primes. In this paper, we consider a more general setting. Let $K$ be an algebraic number field, $\mathcal O_K$ its ring of integers, $\mathfrak p\subset \mathcal O$ a nonzero prime ideal, and $\mathcal O_{\mathfrak p}$ the localization of $\mathcal O$ at $\mathfrak p$. We investigate when the group ring $\mathcal O_{\mathfrak p}[G]$ is weakly clean and feebly clean, where $G$ is a finite abelian group, and establish an explicit characterization for such a group ring to be weakly clean and feebly clean for the case when $K=\mathbb Q(ζ_n)$ is a cyclotomic field or $K=\mathbb Q(\sqrt{d})$ is a quadratic field.

math.RA↗

arXiv2019

Clean group rings over localizations of rings of integers

A ring $R$ is said to be clean if each element of $R$ can be written as the sum of a unit and an idempotent. In a recent article (J. Algebra, 405 (2014), 168-178), Immormino and McGoven characterized when the group ring $\mathbb Z_{(p)}[C_n]$ is clean, where $\mathbb Z_{(p)}$ is the localization of the integers at the prime $p$. In this paper, we consider a more general setting. Let $K$ be an algebraic number field, $\mathcal O_K$ be its ring of integers, and $R$ be a localization of $\mathcal O_K$ at some prime ideal. We investigate when $R[G]$ is clean, where $G$ is a finite abelian group, and obtain a complete characterization for such a group ring to be clean for the case when $K=\mathbb Q(ζ_n)$ is a cyclotomic field or $K=\mathbb Q(\sqrt{d})$ is a quadratic field.

math.RA↗

arXiv2017

Zero-sum invariants of finite abelian groups

The purpose of the article is to provide an unified way to formulate zero-sum invariants. Let $G$ be a finite additive abelian group. Let $B(G)$ denote the set consisting of all nonempty zero-sum sequences over G. For $Ω\subset B(G$), let $d_Ω(G)$ be the smallest integer $t$ such that every sequence $S$ over $G$ of length $|S|\geq t$ has a subsequence in $Ω$.We provide some first results and open problems on $d_Ω(G)$.

math.CO↗

arXiv2015

Noetherian Rings Whose Annihilating-Ideal Graphs Have finite Genus

Let $R$ be a commutative ring and ${\Bbb{A}}(R)$ be the set of ideals with non-zero annihilators. The annihilating-ideal graph of $R$ is defined as the graph ${\Bbb{AG}}(R)$ with vertex set ${\Bbb{A}}(R)^*={\Bbb{A}}\setminus\{(0)\}$ such that two distinct vertices $I$ and $J$ are adjacent if and only if $IJ=(0)$. We characterize commutative Noetherian rings $R$ whose annihilating-ideal graphs have finite genus $γ(\Bbb{AG}(R))$. It is shown that if $R$ is a Noetherian ring such that $0<γ(\Bbb{AG}(R))<\infty$, then $R$ has only finitely many ideals.

math.RA↗

arXiv2014

On zero divisors and prime elements of po-semirings

A semiring is an algebraic structure similar to a ring, but without the requirement that each element must have an additive inverse. A po-semiring is a semiring equipped with a compatible bounded partial order. In this paper, properties of zero divisors and prime elements of a po-semiring are studied. In particular, it is proved that under some mild assumption the set $Z(A)$ of nonzero zero divisors of $A$ is $A\setminus \{0,1\}$, each prime element of $A$ is a maximal element, and the zero divisor graph $\G(A)$ of $A$ is a finite graph if and only if $A$ is finite. For a po-semiring $A$ with $Z(A)=A\setminus \{0,1\}$, it is proved that $A$ has finitely many maximal elements if ACC holds either for elements of $A$ or for principal annihilating ideals of $A$. As applications of prime elements, it is shown that the structure of a po-semiring $A$ is completely determined by the structure of integral po-semirings if either $|Z(A)|=1$ or $|Z(A)|=2$ and $Z(A)^2\not=0$. Applications to the ideal structure of commutative rings are considered.

math.RA↗

arXiv2014

On the index of length four minimal zero-sum sequences

Let $G$ be a finite cyclic group. Every sequence $S$ over $G$ can be written in the form $S=(n_1g)\cdot\ldots\cdot(n_lg)$ where $g\in G$ and $n_1, \ldots, n_l\in[1, \ord(g)]$, and the index $\ind(S)$ of $S$ is defined to be the minimum of $(n_1+\cdots+n_l)/\ord(g)$ over all possible $g\in G$ such that $\langle g \rangle =G$. A conjecture on the index of length four sequences says that every minimal zero-sum sequence of length 4 over a finite cyclic group $G$ with $\gcd(|G|, 6)=1$ has index 1. The conjecture was confirmed recently for the case when $|G|$ is a product of at most two prime powers. However, the general case is still open. In this paper, we make some progress towards solving the general case. Based on earlier work on this problem, we show that if $G=\langle g\rangle$ is a finite cyclic group of order $|G|=n$ such that $\gcd(n,6)=1$ and $S=(x_1g)(x_2g)(x_3g)(x_4g)$ is a minimal zero-sum sequence over $G$ such that $x_1,\cdots,x_4\in[1,n-1]$ with $\gcd(n,x_1,x_2,x_3,x_4)=1$, and $\gcd(n,x_i)>1$ for some $i\in[1,4]$, then $\ind(S)=1$. By using an innovative method developed in this paper, we are able to give a new (and much shorter) proof to the index conjecture for the case when $|G|$ is a product of two prime powers.

math.NT↗

arXiv2014

Minimal zero-sum sequence of length five over finite cyclic groups of prime power order

Let $G$ be a finite cyclic group. Every sequence $S$ of length $l$ over $G$ can be written in the form $S=(x_1g)\cdot\ldots\cdot(x_lg)$ where $g\in G$ and $x_1, \ldots, x_l\in[1, \ord(g)]$, and the index $\ind(S)$ of $S$ is defined to be the minimum of $(x_1+\cdots+x_l)/\ord(g)$ over all possible $g\in G$ such that $\langle g \rangle =G$. Recently the second and the third authors determined the index of any minimal zero-sum sequence $S$ of length 5 over a cyclic group of a prime order where $S=g^2(x_2g)(x_3g)(x_4g)$. In this paper, we determine the index of any minimal zero-sum sequence $S$ of length 5 over a cyclic group of a prime power order. It is shown that if $G=\langle g\rangle$ is a cyclic group of prime power order $n=p^μ$ with $p \geq 7$ and $μ\geq 2$, and $S=(x_1g)(x_2g)(x_2g)(x_3g)(x_4g)$ with $x_1=x_2$ is a minimal zero-sum sequence with $\gcd(n,x_1,x_2,x_3,x_4,x_5)=1$, then $\ind(S)=2$ if and only if $S=(mg)(mg)(m\frac{n-1}{2}g)(m\frac{n+3}{2}g)(m(n-3)g)$ where $m$ is a positive integer such that $\gcd(m,n)=1$.

math.NT↗

arXiv2013

An upper bound for Davenport constant of finite groups

Let $G$ be a finite (not necessarily abelian) group and let $p=p(G)$ be the smallest prime number dividing $|G|$. We prove that $d(G)\leq \frac{|G|}{p}+9p^2-10p$, where $d(G)$ denotes the small Davenport constant of $G$ which is defined as the maximal integer $\ell$ such that there is a sequence over $G$ of length $\ell$ contains no nonempty one-product subsequence.

math.NT↗