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Xiaolei Zhang

Publications and source records attributed to Xiaolei Zhang.

At least 37 records · Page 2Linked to original sources
arXiv2026

The small finitistic dimensions of commutative rings, III

The small finitistic dimension fPD$(R)$ of a ring $R$ is defined to be the supremum of projective dimensions of $R$-modules with finite projective resolutions. In this paper, we show that a commutative ring $R$ has fPD$(R)\leq d$ if and only if for any finitely generated ideal $I$ of $R$, if $Ext_R^i(R/I,R)=0$ for each $i=0,\dots,d$, then $Ext_R^i(R/I,R)=0$ for all $i\geq 0.$ As applications, we obtain that, for any commutative ring $R$, fPD$(R)\leq \mbox{FP-}Id_RR$, the self-FP-injective dimension of $R$. We also give some applications of these results to (weak) $(n,d)$-rings, DW-rings and rings of Prufer type.

math.AC↗
arXiv2026

Relative Faithful Exact Functors and Their Applications to Homological Modules

The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and exact--play fundamental roles across various areas of algebra. In this paper, we extend these notions to the setting of $w$-operation theory. By introducing the concept of $w$-faithfully exact functors, we define and investigate the notions of $w$-faithfully projective, $w$-faithfully flat, and $w$-faithfully injective modules. We establish their fundamental properties and demonstrate their effectiveness in generalizing classical results.

math.AC↗
arXiv2026

Almost Noetherian rings and modules

In this paper, we investigate the notions of almost Noetherian rings and modules. In details, we give the Cohen type theorem, Eakin-Nagata type theorem, Kaplansky type Theorem and Hilbert basis theorem and some other rings constructions for almost Noetherian rings. In particular, we resolve a question proposed in \cite[9, B. Zavyalov, {\it Almost coherent modules and almost coherent sheaves}, Memoirs of the European Mathematical Society 19. Berlin: European Mathematical Society (EMS), 2025] under a certain condition.

math.AC↗
arXiv2026

A survey on the uniform $S$-version of rings, modules and their homological theories

This survey provides a comprehensive overview of the recent advancements in the theory of ``uniformly $S$''-algebraic structures in commutative ring theory. Originating from the classical concepts of Noetherian, coherent, von Neumann regular, and semisimple rings, the introduction of a multiplicative subset $S$ has led to the development of $S$-Noetherian, $S$-coherent, and other $S$-analogues. However, the element $s \in S$ in the original definitions often depends on the ideal or module under consideration. To overcome this limitation and enable deeper module-theoretic characterizations, the notion of "uniformly $S$" (abbreviated as $u$-$S$) was introduced. This survey systematically presents the definitions, characterizations, and properties of $u$-$S$-torsion modules, $u$-$S$-exact sequences, and the subsequent uniform analogues of fundamental module classes: $u$-$S$-finitely presented, $u$-$S$-Noetherian, $u$-$S$-coherent, $u$-$S$-flat, $u$-$S$-projective, $u$-$S$-injective, and $u$-$S$-absolutely pure modules. We then explore the associated uniform homological dimensions, including the $u$-$S$-weak global dimension, the $u$-$S$-global dimension, and their interplay with polynomial rings and localizations. The survey also covers structural ring classes such as $u$-$S$-von Neumann regular, $u$-$S$-semisimple, $u$-$S$-Artinian, $u$-$S$-multiplication rings, and rings with $u$-$S$-Noetherian spectrum.

math.AC↗
arXiv2026

CODE: A Contradiction-Based Deliberation Extension Framework for Overthinking Attacks on Retrieval-Augmented Generation

Introducing reasoning models into Retrieval-Augmented Generation (RAG) systems enhances task performance through step-by-step reasoning, logical consistency, and multi-step self-verification. However, recent studies have shown that reasoning models suffer from overthinking attacks, where models are tricked to generate unnecessarily high number of reasoning tokens. In this paper, we reveal that such overthinking risk can be inherited by RAG systems equipped with reasoning models, by proposing an end-to-end attack framework named Contradiction-Based Deliberation Extension (CODE). Specifically, CODE develops a multi-agent architecture to construct poisoning samples that are injected into the knowledge base. These samples 1) are highly correlated with the use query, such that can be retrieved as inputs to the reasoning model; and 2) contain contradiction between the logical and evidence layers that cause models to overthink, and are optimized to exhibit highly diverse styles. Moreover, the inference overhead of CODE is extremely difficult to detect, as no modification is needed on the user query, and the task accuracy remain unaffected. Extensive experiments on two datasets across five commercial reasoning models demonstrate that the proposed attack causes a 5.32x-24.72x increase in reasoning token consumption, without degrading task performance. Finally, we also discuss and evaluate potential countermeasures to mitigate overthinking risks.

cs.CR↗
arXiv2026

Almost coherent rings

Inspired from the work of P. Scholze on the finiteness of \(\mathbf{F}_{p}\)-cohomology groups of proper rigid-analytic varieties over \(p\)-adic fields, Zavyalov recently introduced the notion of almost coherent rings, which plays a key role in the almost ring theory. In this paper, we characterize almost coherent rings in terms of almost flat modules and almost absolutely pure modules, integrating numerous classical results into almost mathematics. Besides, we show that every almost coherent $R$-module is not almost isomorphic to a coherent $R$-module, giving a negative answer to a question proposed in [14,B. Zavyalov, {\it Almost coherent modules and almost coherent sheaves}, Memoirs of the European Mathematical Society 19. Berlin: European Mathematical Society (EMS), 2025].

math.AC↗
arXiv2026

Some remarks on $u$-$S$-Noetherian and $u$-$S$-coherent rings

In this paper, we give some new characterizations of $u$-$S$-Noetherian rings and $u$-$S$-coherent rings in terms of uniform $S$-version of injective precovers, flat preenvelopes and absolutely pure modules, respectively. Moreover, we give a negative answer to a question proposed by Bouziri [3].

math.AC↗
arXiv2025

Perturbation Self-Supervised Representations for Cross-Lingual Emotion TTS: Stage-Wise Modeling of Emotion and Speaker

Cross-lingual emotional text-to-speech (TTS) aims to produce speech in one language that captures the emotion of a speaker from another language while maintaining the target voice's timbre. This process of cross-lingual emotional speech synthesis presents a complex challenge, necessitating flexible control over emotion, timbre, and language. However, emotion and timbre are highly entangled in speech signals, making fine-grained control challenging. To address this issue, we propose EMM-TTS, a novel two-stage cross-lingual emotional speech synthesis framework based on perturbed self-supervised learning (SSL) representations. In the first stage, the model explicitly and implicitly encodes prosodic cues to capture emotional expressiveness, while the second stage restores the timbre from perturbed SSL representations. We further investigate the effect of different speaker perturbation strategies-formant shifting and speaker anonymization-on the disentanglement of emotion and timbre. To strengthen speaker preservation and expressive control, we introduce Speaker Consistency Loss (SCL) and Speaker-Emotion Adaptive Layer Normalization (SEALN) modules. Additionally, we find that incorporating explicit acoustic features (e.g., F0, energy, and duration) alongside pretrained latent features improves voice cloning performance. Comprehensive multi-metric evaluations, including both subjective and objective measures, demonstrate that EMM-TTS achieves superior naturalness, emotion transferability, and timbre consistency across languages.

cs.SD↗
arXiv2025

Module-Theoretic Characterizations of Prufer $v$-Multiplication Domains

We present unified $w$-theoretic characterizations of Prüfer $v$-multiplication domains (P$v$MDs). A module-theoretic perspective shows that torsion submodules are $w$-pure, and for $(w$-)$\,$finitely generated modules $M$, the canonical sequence $0\to T(M)\to M\to M/T(M)\to 0$ $w$-splits, resolving an open question of Geroldinger--Kim--Loper. In a $w$-version of Hattori-Davis theory, these conditions are equivalent to $Tor^R_2(M,N)$ being $GV$-torsion for all $R$-modules $M,N$, equivalently $w$-w.gl.dim$(R)\leq 1$, or $Tor^R_1(X,A)$ being $GV$-torsion for all $X$ and torsion-free $A$, or the Davis map $A\otimes_R B \to \mathcal T\otimes_K \mathcal S$ having $GV$-torsion kernel. From an overring viewpoint, $R$ is a P$v$MD if and only if for every $R\subseteq T\subseteq K$ and every $w$-maximal ideal $m$, the localization $R_{m}\to T_{\m}$ is a flat epimorphism, so that each overring is $w$-flat and the inclusion is $w$-epimorphic. Finally, $R$ is a P$v$MD if and only if every pure $w$-injective divisible $R$-module is injective.

math.AC↗
arXiv2025

Rings with uniformly S-w-Noetherian spectrum

In this paper, the notion of rings with uniformly S-w-Noetherian spectrum is introduced. Several characterizations of rings with uniformly S-w-Noetherian spectrum are given. Actually, we show that a ring R has uniformly S-w-Noetherian spectrum with respect to some s 2 S if and only if each ascending chain of radical w-ideals of R is stationary with respect to s 2 S, if and only if each radical (prime) (w-)ideal of R is radically S-w-finite with respect to s, if and only if each countably generated ideal of R is radically S-w-finite with respect to s, if and only if R[X] has uniformly S-w-Noetherian spectrum, if and only if RfXg has uniformly S-Noetherian spectrum. Beside, we show a ring R has Noetherian (resp., uniformly S-Noetherian) spectrum with respect to s if and only if each countably generated ideal of R is radically finite (S-finite with respect to s), which is a new result in the classical case.

math.AC↗
arXiv2025

$\text{M}^3\text{PDB}$: A Multimodal, Multi-Label, Multilingual Prompt Database for Speech Generation

Recent advancements in zero-shot speech generation have enabled models to synthesize speech that mimics speaker identity and speaking style from speech prompts. However, these models' effectiveness is significantly limited in real-world scenarios where high-quality speech prompts are absent, incomplete, or out of domain. This issue arises primarily from a significant quality mismatch between the speech data utilized for model training and the input prompt speech during inference. To address this, we introduce $\text{M}^3\text{PDB}$, the first large-scale, multi-modal, multi-label, and multilingual prompt database designed for robust prompt selection in speech generation. Our dataset construction leverages a novel multi-modal, multi-agent annotation framework, enabling precise and hierarchical labeling across diverse modalities. Furthermore, we propose a lightweight yet effective prompt selection strategy tailored for real-time, resource-constrained inference settings. Experimental results demonstrate that our proposed database and selection strategy effectively support various challenging speech generation scenarios. We hope our work can inspire the community to shift focus from improving performance on standard benchmarks to addressing more realistic and diverse application scenarios in speech generation. Code and dataset are available at: https://github.com/hizening/M3PDB.

eess.AS↗
arXiv2025

Cardiac-CLIP: A Vision-Language Foundation Model for 3D Cardiac CT Images

Foundation models have demonstrated remarkable potential in medical domain. However, their application to complex cardiovascular diagnostics remains underexplored. In this paper, we present Cardiac-CLIP, a multi-modal foundation model designed for 3D cardiac CT images. Cardiac-CLIP is developed through a two-stage pre-training strategy. The first stage employs a 3D masked autoencoder (MAE) to perform self-supervised representation learning from large-scale unlabeled volumetric data, enabling the visual encoder to capture rich anatomical and contextual features. In the second stage, contrastive learning is introduced to align visual and textual representations, facilitating cross-modal understanding. To support the pre-training, we collect 16641 real clinical CT scans, supplemented by 114k publicly available data. Meanwhile, we standardize free-text radiology reports into unified templates and construct the pathology vectors according to diagnostic attributes, based on which the soft-label matrix is generated to supervise the contrastive learning process. On the other hand, to comprehensively evaluate the effectiveness of Cardiac-CLIP, we collect 6,722 real-clinical data from 12 independent institutions, along with the open-source data to construct the evaluation dataset. Specifically, Cardiac-CLIP is comprehensively evaluated across multiple tasks, including cardiovascular abnormality classification, information retrieval and clinical analysis. Experimental results demonstrate that Cardiac-CLIP achieves state-of-the-art performance across various downstream tasks in both internal and external data. Particularly, Cardiac-CLIP exhibits great effectiveness in supporting complex clinical tasks such as the prospective prediction of acute coronary syndrome, which is notoriously difficult in real-world scenarios.

eess.IV↗
arXiv2025

Understanding the fill-factor limit of organic solar cells

Although the power conversion efficiencies of organic solar cells (OSCs) have surpassed 20%, they still lag behind commercial inorganic solar cells and emerging perovskite solar cells. To bridge this efficiency gap, improving the fill factor (FF) is critical, provided other photovoltaic parameters are not compromised. However, the fundamental understanding of the FF in OSCs remains incomplete. In this work, we systematically investigate a wide range of OSCs with the FF values spanning 0.27 to 0.80, and analyse the effect of free charge generation and recombination on the FF in OSCs. To explain our observations, we developed an analytical model that quantitatively correlates the applied electric field with the energetics of excited states in donor-acceptor blends. By combining device characterisation, spectroscopy, and theoretical modelling, we reveal that the Stark effect and the field-dependent charge transfer significantly impact the FF in state-of-the-art OSCs with low voltage losses. Our findings highlight that suppressing geminate decay by increasing exciton lifetime is a promising strategy for boosting the FF and achieving future efficiency gains in OSCs.

cond-mat.mtrl-sci↗
arXiv2025

Automatic Classification and Segmentation of Tunnel Cracks Based on Deep Learning and Visual Explanations

Tunnel lining crack is a crucial indicator of tunnels' safety status. Aiming to classify and segment tunnel cracks with enhanced accuracy and efficiency, this study proposes a two-step deep learning-based method. An automatic tunnel image classification model is developed using the DenseNet-169 in the first step. The proposed crack segmentation model in the second step is based on the DeepLabV3+, whose internal logic is evaluated via a score-weighted visual explanation technique. Proposed method combines tunnel image classification and segmentation together, so that the selected images containing cracks from the first step are segmented in the second step to improve the detection accuracy and efficiency. The superior performances of the two-step method are validated by experiments. The results show that the accuracy and frames per second (FPS) of the tunnel crack classification model are 92.23% and 39.80, respectively, which are higher than other convolutional neural networks (CNN) based and Transformer based models. Also, the intersection over union (IoU) and F1 score of the tunnel crack segmentation model are 57.01% and 67.44%, respectively, outperforming other state-of-the-art models. Moreover, the provided visual explanations in this study are conducive to understanding the "black box" of deep learning-based models. The developed two-stage deep learning-based method integrating visual explanations provides a basis for fast and accurate quantitative assessment of tunnel health status.

cs.CV↗
arXiv2025

On the existence of parameterized noetherian rings

A ring $R$ is called left strictly $(<\aleph_α)$-noetherian if $\aleph_α$ is the minimum cardinal such that every ideal of $R$ is $(<\aleph_α)$-generated. In this note, we show that for every singular (resp., regular) cardinal $\aleph_α$, there is a valuation domain $D$, which is strictly $(<\aleph_α)$-noetherian (resp., strictly $(<\aleph_α^+)$-noetherian), positively answering a problem proposed in \cite{Marcos25} under some set theory assumption.

math.RA↗
arXiv2024

On (uniformly) $S$-$w$-Noetherian rings and modules

Let $R$ be a ring and $S$ a multiplicative subset of $R$. We introduce and study the notions of ($u$-)$S$-$w$-Noetherian modules and ($u$-)$S$-$w$-principal ideal modules. Some characterizations of these new concepts are given.

math.AC↗
arXiv2024

Some new module-theoretic characterizations of $S$-coherent rings

Let $R$ be a commutative ring with identity and $S$ a multiplicative subset of $R$. In this paper, we first introduce and study the notions of $s$-pure exact sequences and $s$-absolutely pure modules which extend the classical notions of pure exact sequences and absolutely pure modules. And then, we give some new characterizations of $S$-coherent rings in terms of $s$-absolutely pure modules.

math.AC↗