arXiv subjects

Yu Qiu

Publications and source records attributed to Yu Qiu.

At least 19 recordsLinked to original sources

arXiv2026

$\mathrm{X}$-evolution flows/foliations for cluster algebras: partial Bongartz (co-)completions and acyclicity

We first generalize the notion of $\mathrm{X}$-foliation on cluster complexes to the context of cluster algebras. This is a continuous generalization of Keller's green mutation, which was previously introduced in the prequel within a categorical setting. We show that the wall-crossing structure (of possibly higher co-dimension) is encoded by $\mathrm{X}$-supports, which form a partial version of Cao-Gyoda-Yurikusa's Bongartz (co-)completions for cluster algebras. Moreover, we prove that for any cell transversed nontrivially by a fixed $\mathrm{X}$-leaf, its rank is an invariant bounded below by the rank of $\mathrm{X}$. Finally, we prove the acyclicity conjecture for $\mathrm{X}$-foliation, which also implies the compactness conjecture for any $\mathrm{X}$-foliation in finite type cases.

math.RT↗

arXiv2026

Topological Models for Categories Associated with the Weighted Projective Lines of Type $(2,2,2,2)$

We construct a geometric model for the derived category of the weighted projective line $\mathbb{CP}^1_ω$ of type $(2,2,2,2)$ using a graded sphere with four binaries. More precisely, we give a bijection between the set of indecomposable rigid objects and the set of certain arcs, such that the dimensions of $\operatorname{Hom}$-spaces are computed by oriented intersection numbers. As applications, we provide a geometric realization of the indecomposable rigid objects in the cluster category $\mathcal{C}(\mathbb{CP}^1_ω)$ via tagged arcs on the four-punctured sphere, with $\operatorname{Hom}$-space dimensions given by tagged intersection numbers. When the weighted points of $\mathbb{CP}^1_ω$ are $(0,1,\infty,\frac{1}{2})$, both correspondences are compatible with the natural actions of the automorphism groups and the corresponding mapping class groups.

math.RT↗

arXiv2026

LYRA: Label-Free Structural Synchronization and Resource Allocation for UAV Edge Networks

While deploying hierarchical vision models to process mission-critical tasks, UAV edge systems must adaptively update the models to sustain inference reliability under low-level environmental corruption. However, existing work has overlooked the optimal timing for model updates, the impracticality of relying on real-time expert labels, and the significant bandwidth and energy constraints of UAVs. This paper proposes a joint model update scheduling and resource allocation framework, aiming to maximize long-term semantic fidelity and resource efficiency of UAV edge intelligence systems. To address the challenge of label-free semantic evaluation, we formulate the Online Semantic Disagreement Rate (OSDR) as a proxy for timely update triggering, thereby enabling fine-grained Sensitivity-Aware Structural Synchronization (SASS). Furthermore, to overcome the curse of dimensionality in hybrid action spaces and effectively bound long-term energy budgets, we propose a Lyapunov-guided discrete reinforcement learning algorithm that performs action space dimensionality reduction and transforms constraints into virtual queue stability problems. The reported experimental results, based on real traffic traces, demonstrate that the proposed framework consistently outperforms representative baselines in semantic recovery efficiency and update triggering precision, by satisfying long-term energy budget and by reducing average risk backlog by up to 33.3\% in the dynamic environmental corruption scenario.

cs.NI↗

arXiv2026

Moduli spaces of quadratic differentials: Abel-Jacobi map and deformation

We study the moduli space of framed quadratic differentials with prescribed singularities parameterized by a decorated marked surface with punctures (DMSp), where simple zeros, double poles and higher order poles respectively correspond to decorations, punctures and boundary components. We show that the fundamental group of this space equals the kernel of the Abel-Jacobi (AJ) map from the surface mapping class group of DMSp to the first homology group of the marked surface (without decorations/punctures). Moreover, a universal cover of this space is given by the space of stability conditions on the associated 3-Calabi-Yau category. Furthermore, when we partially compactify and orbifold this moduli space by allowing the collision of simple zeros and some of the double poles, the resulting moduli space is isomorphic to a quotient of the space of stability conditions on the deformed (with respect to those collidable double poles) 3-Calabi-Yau category. Finally, we show that the fundamental group of this partially compactified orbifold equals the quotient group of the kernel of the AJ map by the square of any point-pushing diffeomorphism around any collidable double pole. This construction can produces any non-exceptional spherical/Euclidean Artin braid groups.

math.GT↗

arXiv2026

UD-ASD: A Unified Diffusion Model for Anomalous Sound Detection

Anomalous Sound Detection (ASD) aims to determine whether faults have occurred by monitoring sounds. Existing methods detect a limited range of anomalies, exhibit poor generalization, or train a separate model for each machine. Diffusion models possess strong generalization and can generate specific data with condition guidance. We propose a unified diffusion model only with a small module. The audio is first transformed into log-Mel spectrograms. The lightweight module embeds machine IDs into condition embeddings, guiding the model to reconstruct data for specific machines. Then diffusion model reconstructs data with condition, using Gaussian Mixture Models to fit the distributions of reconstruction errors. Our unified model could monitor multiple machine types and learn more fundamental feature spaces with cross-domain learning. Experiments on DCASE2022 Challenge Task 2 show that our model achieves 3.44% AUC and 2.52% pAUC improvements over baseline, validating its effectiveness.

cs.SD↗

arXiv2026

Perverse schobers, stability conditions and quadratic differentials I

We develop a unified approach for identifying spaces of stability conditions of triangulated categories arising from weighted marked surfaces with moduli spaces of quadratic differentials. This identification is based on the use of perverse schobers (perverse sheaves of triangulated categories) and a notion of positive arc system kit on a perverse schober $\mathcal F$, which provides a systematic way of assigning to a graded curve on the surface a global section of $\mathcal F$. This assignment allows us to identify mixed-angulations and their flips with finite-length hearts and their tilts. As an application we obtain a generalization of the results of Bridgeland--Smith to quadratic differentials with arbitrary singularity type (zero/pole/exponential).

math.RT↗

arXiv2026

Satellite quenching by radio jets of central galaxies in galaxy groups

Feedback from active galactic nuclei (AGN) is now recognized as a key component of galaxy formation models. It plays a central role in regulating the growth and quenching of galaxies in the center of groups. However, the impact of AGN feedback from central galaxies on satellite galaxies remains largely unexplored. Here based on the largest sample to date of radio AGNs in galaxy groups (Yang et al. 2007) and a comprehensive consideration of multiple physical parameters that may influence the star formation of satellite galaxies, we demonstrate that the quiescent satellite fraction around radio AGNs is higher than that around normal galaxies. The most significant enhancement is observed around AGNs with large radio lobes. These findings demonstrate that the impact of kinetic AGN feedback beyond their host galaxies to their satellites. These results provide novel insights into the physical origins of some long-standing puzzles in extragalactic astronomy, including, e.g., galactic conformity and the strong small-scale clustering of quiescent galaxies.

astro-ph.GA↗

arXiv2026

Verdier quotients of Calabi-Yau categories from quivers with potential

We study a class of triangulated categories obtained as Verdier quotients of 3-Calabi-Yau categories combinatorially described by quivers with potential from (decorated) marked surfaces. We study their bounded t-structures and consider in particular the exchange graphs of hearts and silting objects, and show that the Koszul isomorphism between these graphs is preserved under Verdier quotient.

math.RT↗

arXiv2026

Non-asphericity of strata of genus-one differentials and stability spaces

We show that when the number of zeros or poles is at least four, every connected component of the strata of differentials in genus one with prescribed zero and pole orders is not an orbifold $K(π,1)$. For quadratic differentials, this provides infinitely many counterexamples to a conjecture attributed to Kontsevich, as well as to a folklore conjecture concerning the contractibility of spaces of Bridgeland stability conditions.

math.GT↗

arXiv2026

DeepInsight: A Unified Evaluation Infrastructure Across the Physical AI Stack

Evaluating a Physical AI stack spans operators that differ by more than three orders of magnitude -- from a single foundation-model decoding step to thousands of physics ticks of whole-body control -- varying orthogonally in modality, reward semantics, and resource profile. No existing framework spans this range, so the stack is evaluated today by stitching together separate harnesses that share neither runtime nor scoring, preserving each segment's local validity but losing the shared identity needed to diagnose cross-layer regressions. We present DeepInsight, an evaluation infrastructure that serves this full spectrum on a single runtime. Rather than homogenize the regimes, it preserves their heterogeneity behind three narrow abstractions -- task, resource, and result -- each realized as one invariant shared by every subsystem: one episode driver, one resource-handle protocol implemented by every expensive backend (LLM inference and sandboxed runtimes alike), and one trace identity scheme under which every event is written. Deployed in production across all three layers of an embodied humanoid stack, this single set of invariants onboards new benchmarks largely by configuration. Where mature peer orchestrators exist -- at the foundation-model end -- it reproduces published references and peer-framework readings within their own spread, runs the same suites faster on a single node, and scales near-linearly across nodes. Its distinctive return is diagnostic: because every layer writes into one shared trace, a regression that begins in one layer and surfaces in another stays localizable on that trace -- a cross-layer payoff no federation of per-segment harnesses can reproduce.

cs.AI↗

arXiv2026

Perverse schobers, stability conditions and quadratic differentials II: relative graded Brauer graph algebras

We introduce a class of dg-algebras which generalize the classical Brauer graph algebras. They are constructed from mixed-angulations of surfaces and often admit a (relative) Calabi--Yau structure. We discovered these algebras through two very distinct routes, one involving perverse schobers whose stalks are cyclic quotients of the derived categories of relative Ginzburg algebras, and another involving deformations of partially wrapped Fukaya categories of surfaces. Applying the results of our previous work arXiv:2303.18249, we describe the spaces of stability conditions on the derived categories of these algebras in terms of spaces of quadratic differentials.

math.RT↗

arXiv2025

Decorated Marked Surfaces with vortices: Cluster braid group vs. braid twist group

Let $\mathbf{S}$ be a marked surface with vortices (=punctures with extra $\mathbb{Z}_2$ symmetry). We study the decorated version $\mathbf{S}_\bigtriangleup$, where the $\mathbb{Z}_2$ symmetry lifts to the relation that the fourth power of the braid twist of any collision path (connecting a decoration in $\bigtriangleup$ and a vortex) is identity. We prove the following three groups are isomorphic: King-Qiu's cluster braid group associated to $\mathbf{S}$, the braid twist group of $\mathbf{S}_\bigtriangleup$ and the fundamental group of Bridgeland-Smith's moduli space of $\mathbf{S}$-framed GMN differentials. Moreover, we give finite presentations of such groups.

math.RT↗

arXiv2025

Quadratic Differentials as Stability Conditions of Graded Skew-gentle Algebras

We prove that the principal component of the exchange graph of hearts of a graded skew-gentle algebra can be identified with the corresponding exchange graph of S-graphs, using the geometric models and the intersection formula in \cite{QZZ}. Using the similar argument in \cite{BS, BMQS, CHQ}, we extend this identification to an isomorphism between the spaces of stability conditions and of quadratic differentials.

math.RT↗

arXiv2025

Reduced Gas Accretion onto Galaxies due to Effects of External Giant Radio Lobes

Suppression effects of giant radio lobes from supermassive black holes on gas accretion onto galaxies in the surrounding regions are quantified using cosmological magneto-hydrodynamic simulations. With an appropriate amount of radio jet energy injected into the intergalactic medium following the formation peak of supermassive black holes at redshift two, we find that galaxies in the greater neighborhood of the jet-launching massive galaxies subsequently experience a significant reduction in the amount of accreted gas. The distribution of the resulting magnetic field in the intergalactic medium is highly inhomogeneous, due to the highly biased nature of the most massive supermassive black holes. In regions with magnetic field strength $B>10^{-2}μ$G, the baryon fraction is on average reduced by 17%, 14%, and 12%, respectively, for halos of mass in the range of $[10^{11}-10^{12})\msun$, $[10^{12}-10^{13})\msun$, and $[10^{13}-10^{14})\msun$. A proper inclusion of this new, external, global, preventive feedback mechanism from AGN in the next generation of cosmological simulation may be necessary.

astro-ph.GA↗

arXiv2025

From green mutation to $\mathrm{X}$-evolution: flows and foliations on cluster complexes

For any point $\mathrm{X}$ in the cluster complex $\mathrm{Cpx}(\mathcal{C})$ of a 2-Calabi-Yau category $\mathcal{C}$, we introduce $\mathrm{X}$-evolution flow on $\mathrm{Cpx}(\mathcal{C})$. We show that such a flow induces a piecewise linear one-dimensional $\mathrm{X}$-foliation with two singularities, the unique sink $\mathrm{X}$ and the unique source $\mathrm{X}[1]$. Moreover, we show that evolution flows on cluster complexes are continuous refinement/generalization of green mutations on cluster exchange graphs. For the cluster category of a Dynkin or Euclidean quiver $Q$, we prove that the $\mathrm{X}$-foliation is compact or semi-compact, for various choices of $\mathrm{X}$. As an application, we show that $\mathrm{Cpx}(\mathcal{C})$ is spherical (Dynkin case) or contractible (Euclidean case). As a byproduct, we show that the fundamental group of the cluster exchange graph of $Q$ is generated by squares and pentagons.

math.RT↗

arXiv2025

Beyond path selection: Better LLMs for Scientific Information Extraction with MimicSFT and Relevance and Rule-induced(R$^2$)GRPO

Previous study suggest that powerful Large Language Models (LLMs) trained with Reinforcement Learning with Verifiable Rewards (RLVR) only refines reasoning path without improving the reasoning capacity in math tasks while supervised-finetuning(SFT) with distillation can. We study this from the view of Scientific information extraction (SciIE) where LLMs and reasoning LLMs underperforms small Bert-based models. SciIE require both the reasoning and memorization. We argue that both SFT and RLVR can refine the reasoning path and improve reasoning capacity in a simple way based on SciIE. We propose two-stage training with 1. MimicSFT, using structured reasoning templates without needing high-quality chain-of-thought data, 2. R$^2$GRPO with relevance and rule-induced rewards. Experiments on scientific IE benchmarks show that both methods can improve the reasoning capacity. R$^2$GRPO with mimicSFT surpasses baseline LLMs and specialized supervised models in relation extraction. Our code is available at https://github.com/ranlislz/R2GRPO.

cs.CL↗

arXiv2025

Salient Object Detection in Traffic Scene through the TSOD10K Dataset

Traffic Salient Object Detection (TSOD) aims to segment the objects critical to driving safety by combining semantic (e.g., collision risks) and visual saliency. Unlike SOD in natural scene images (NSI-SOD), which prioritizes visually distinctive regions, TSOD emphasizes the objects that demand immediate driver attention due to their semantic impact, even with low visual contrast. This dual criterion, i.e., bridging perception and contextual risk, re-defines saliency for autonomous and assisted driving systems. To address the lack of task-specific benchmarks, we collect the first large-scale TSOD dataset with pixel-wise saliency annotations, named TSOD10K. TSOD10K covers the diverse object categories in various real-world traffic scenes under various challenging weather/illumination variations (e.g., fog, snowstorms, low-contrast, and low-light). Methodologically, we propose a Mamba-based TSOD model, termed Tramba. Considering the challenge of distinguishing inconspicuous visual information from complex traffic backgrounds, Tramba introduces a novel Dual-Frequency Visual State Space module equipped with shifted window partitioning and dilated scanning to enhance the perception of fine details and global structure by hierarchically decomposing high/low-frequency components. To emphasize critical regions in traffic scenes, we propose a traffic-oriented Helix 2D-Selective-Scan (Helix-SS2D) mechanism that injects driving attention priors while effectively capturing global multi-direction spatial dependencies. We establish a comprehensive benchmark by evaluating Tramba and 22 existing NSI-SOD models on TSOD10K, demonstrating Tramba's superiority. Our research establishes the first foundation for safety-aware saliency analysis in intelligent transportation systems.

cs.CV↗

arXiv2025

Cross-Modal Interactive Perception Network with Mamba for Lung Tumor Segmentation in PET-CT Images

Lung cancer is a leading cause of cancer-related deaths globally. PET-CT is crucial for imaging lung tumors, providing essential metabolic and anatomical information, while it faces challenges such as poor image quality, motion artifacts, and complex tumor morphology. Deep learning-based models are expected to address these problems, however, existing small-scale and private datasets limit significant performance improvements for these methods. Hence, we introduce a large-scale PET-CT lung tumor segmentation dataset, termed PCLT20K, which comprises 21,930 pairs of PET-CT images from 605 patients. Furthermore, we propose a cross-modal interactive perception network with Mamba (CIPA) for lung tumor segmentation in PET-CT images. Specifically, we design a channel-wise rectification module (CRM) that implements a channel state space block across multi-modal features to learn correlated representations and helps filter out modality-specific noise. A dynamic cross-modality interaction module (DCIM) is designed to effectively integrate position and context information, which employs PET images to learn regional position information and serves as a bridge to assist in modeling the relationships between local features of CT images. Extensive experiments on a comprehensive benchmark demonstrate the effectiveness of our CIPA compared to the current state-of-the-art segmentation methods. We hope our research can provide more exploration opportunities for medical image segmentation. The dataset and code are available at https://github.com/mj129/CIPA.

eess.IV↗