arXiv subjects

Ling Wang

Publications and source records attributed to Ling Wang.

At least 19 recordsLinked to original sources

arXiv2026

Asymptotic Expansions of the Fundamental Solution for a Mixed Local-Nonlocal Operator

In this paper, we study the fundamental solution of the mixed local-nonlocal operator $ -\Delta+(-\Delta)^s,$ $ 0<s<1. $ We derive precise asymptotic expansions of the fundamental solution and its gradient, up to the first nontrivial correction term, both near the origin and at infinity. The expansions describe the transition between the local and nonlocal diffusion scales and include the critical regimes in which logarithmic terms occur. As applications of these asymptotics, we establish a distributional B\^ocher-type theorem for nonnegative supersolutions with an isolated singularity. We further obtain quantitative positive and antisymmetric maximum principles on punctured balls.

math.AP↗

arXiv2026

Interior $C^{1,\alpha}$ estimates for the linearized Monge--Amp\`ere equation in two dimensions

We prove an interior $C^{1,\alpha}$ estimate for solutions of the homogeneous linearized Monge--Amp\`ere equation in dimension two under the assumption \[ 0<\lambda\leq \det D^2\varphi\leq\Lambda<+\infty. \] No continuity assumption on the Monge--Amp\`ere density is required. Our result is an affine-invariant analogue of the classical Morrey--Nirenberg $C^{1,\alpha}$ estimate in two dimensions. The core of the proof is the partial Legendre transform. After the transform, the first derivatives of the solution are quotients of adjoint solutions for a uniformly elliptic non-divergence form equation. Bauman's Harnack inequality gives the H\"older control of the quotient, while the Jacobian identity of the partial Legendre transform and a Caccioppoli estimate give its local boundedness. As an application, we prove a Liouville theorem for entire solutions with at most linear growth.

math.AP↗

arXiv2026

Liouville-type theorems for coupled-drift Monge-Amp\`ere equations

In this paper, we study entire solutions and periodic correctors for the coupled-drift Monge-Amp\`ere equation \[ \det D^2u = \exp\{-a\cdot Du+b\cdot x+V(x)-c_0\}, \quad D^2u>0. \] For $V\equiv0$, we obtain a sharp classification of the whole-space solvability regimes: all entire smooth strictly convex solutions are quadratic when $a=b=0$; no such solution exists when $a\neq0$ and $a\cdot b\le0$; and non-quadratic entire solutions exist when $a=0$ and $b\neq0$, or when $a\cdot b>0$. For the null case $a\neq0$, $a\cdot b=0$, we give a scalar maximum-principle argument in every dimension $n\ge2$. For periodic $V$, we prove existence and uniqueness of the normalized pair $(\psi_A,c_A)$ solving the drifted cell problem \[ \det(A+D^2\psi) = \exp\{-a\cdot D\psi+V-c_A\}, \quad A+D^2\psi>0 \quad\text{on }\mathbb T^n. \] We also prove that any asymptotically quadratic entire solution must satisfy $b=Aa$. If its remainder is bounded, then the solution is the corresponding quadratic-periodic corrector up to an additive constant.

math.AP↗

arXiv2026

Min-Max Construction of Anisotropic Minimal Surfaces with Genus Bound

We establish an anisotropic analogue of the celebrated theorem of Meeks-Simon-Yau: every minimizing sequence of surfaces within a fixed isotopy class converges to a smooth stable anisotropic minimal surface, with genus lower semicontinuity. This result also strengthens White's foundational existence theory for anisotropic minimal disks. As an application, we develop an anisotropic Simon-Smith min-max theory. In every closed $3$-manifold, we construct anisotropic min-max sequences within fixed isotopy classes whose limits are stable anisotropic minimal surfaces that are smooth except possibly at a single point. If the integrand satisfies either an ellipticity bound or a $C^3$-pinching condition, we remove the singular point by proving two independent removable singularity theorems for anisotropic minimal surfaces that are smooth and stable away from finitely many points. These removable singularity results also allow to remove the singularities arising in the anisotropic Almgren-Pitts min-max construction in $3$-manifolds of De Philippis-De Rosa and in its multiparameter variants.

math.DG↗

arXiv2026

A Novel Approach to Temporal QoS Estimation via Extended Kalman Filter-Incorporated Latent Feature Analysis

Predicting temporal Quality of Service (QoS) data is critical for optimizing network services and rationalizing resource allocation in cloud computing and service-oriented systems. Existing mainstream methods have achieved promising predictive performance. However, their purely data-driven manner limits their ability to capture non-stationary temporal patterns, thereby leading to accuracy degradation when temporal QoS data exhibits fluctuations. To tackle this limitation, we propose a novel Extended Kalman Filter-Enhanced Latent Feature Analysis (EKL) model to perform efficient and accurate temporal QoS prediction from the perspective of bidirectional model-data-driven learning. Its main idea is three-fold: a) designing a model-driven feature producer to obtain the temporal latent features to capture the intricate temporal pattern following the principle of an Extended Kalman Filter; b) building a data-driven feature producer based on the alternating least squares algorithm to identify time-invariant latent features describing intrinsic user-service characteristics; c) exploiting a density-oriented parallel strategy that achieves workload balancing by sorting users in accordance with their service invocation density, which effectively elevates computational efficiency. In addition, we provide a rigorous theoretical analysis to formally prove the convergence of the proposed EKL. Experimental evaluations conducted on real-world temporal QoS datasets reveal that our proposed EKL surpasses existing state-of-the-art models with respect to both computational efficiency and prediction accuracy for missing temporal QoS data.

cs.LG↗

arXiv2026

SDM-Q: Cost-Aware Staged Decision-Making for Multi-Omics Classification with Deep Q-Learning

Multi-omics data provide complementary molecular characterizations of disease phenotypes and play an important role in disease diagnosis and subtype classification in precision medicine. However, acquiring complete multi-omics profiles is expensive and time-consuming, while most existing deep learning methods assume full modality availability during inference, resulting in substantial redundancy and limited practicality in clinical settings. To address this issue, we propose SDM-Q, a reinforcement learning framework for adaptive and cost-aware multi-omics classification. Specifically, multi-omics diagnosis is reformulated as a finite-horizon sequential decision problem, where the currently acquired omics modalities define the diagnostic state at each stage. An action--value function determines whether to acquire an additional modality or terminate the decision process and output the final prediction. To balance diagnostic utility and acquisition cost, the reward is defined only at the terminal stage and jointly determined by classification correctness and cumulative modality acquisition cost. A backward stage-wise optimization strategy is introduced to improve policy consistency and training stability. Experiments on four public multi-omics datasets, including ROSMAP, LGG, BRCA, and KIPAN, demonstrate that SDM-Q effectively reduces redundant modality acquisition while maintaining competitive classification performance compared with methods using complete multi-omics inputs. In the BRCA and KIPAN datasets, more than 99\% and 95\% of subjects, respectively, achieve accurate classification using only a single omics modality, while the average number of acquired modalities remains below two for ROSMAP and LGG. These results suggest that cost-aware sequential decision-making provides an effective paradigm for improving the efficiency of precision medicine workflows.

cs.LG↗

arXiv2026

QDSP: An Interpretable Structured Learning Framework for Predicting Death or Cerebral Palsy in Very Low Birth Weight Infants

Very low birth weight infants (VLBWI) are at high risk of mortality and severe neurodevelopmental impairment, including cerebral palsy, yet reliable discharge-time prognostic stratification remains challenging in high-dimensional and data-limited clinical settings. To address this problem, we propose QDSP, an interpretable structured learning framework that integrates Quota-guided Subspace Sampling (QSS) and Differentiable-decision-guided Structure Perception (DSP). The QSS module constructs stability-aware and low-redundancy feature subspaces through bootstrap-based feature consistency estimation, whereas the DSP module employs differentiable soft oblique decision structures to model nonlinear clinical interactions while preserving traceable decision evidence. The proposed framework was evaluated on a real-world VLBWI cohort comprising 51 infants and further validated on three public medical tabular datasets. On the primary cohort, QDSP achieved an accuracy of 0.9200 and an AUC of 0.9714, outperforming representative machine learning and deep tabular learning baselines, including XGBoost, TabNet, and TabPFN. Across external datasets, QDSP maintained competitive discrimination and calibration under varying sample sizes and clinical distributions. In addition, SHAP-based analyses and differentiable decision-path tracing identified clinically relevant predictors, including cystic periventricular leukomalacia (cPVL) and birth weight, consistent with established neonatal pathophysiological evidence. These results suggest that QDSP provides an interpretable and robust framework for discharge-time risk stratification in VLBWI and may support early individualized clinical decision-making in neonatal intensive care settings.

cs.LG↗

arXiv2026

Hypergraph Enterprise Agentic Reasoner over Heterogeneous Business Systems

Applying Large Language Models (LLMs) to heterogeneous enterprise systems is hindered by hallucinations and failures in multi-hop, n-ary reasoning. Existing paradigms (e.g., GraphRAG, NL2SQL) lack the semantic grounding and auditable execution required for these complex environments. We introduce HEAR, an enterprise agentic reasoner built on a Stratified Hypergraph Ontology. Its base Graph Layer virtualizes provenance-aware data interfaces, while the Hyperedge Layer encodes n-ary business rules and procedural protocols. Operating an evidence-driven reasoning loop, HEAR dynamically orchestrates ontology tools for structured multi-hop analysis without requiring LLM retraining. Evaluations on supply-chain tasks, including order fulfillment blockage root cause analysis (RCA), show HEAR achieves up to 94.7% accuracy. Crucially, HEAR demonstrates adaptive efficiency: utilizing procedural hyperedges to minimize token costs, while leveraging topological exploration for rigorous correctness on complex queries. By matching proprietary model performance with open-weight backbones and automating manual diagnostics, HEAR establishes a scalable, auditable foundation for enterprise intelligence.

cs.AI↗

arXiv2026

Comparative analysis of missing data imputation methods for CSST survey: Impact on photometric redshift estimation performance

Improving the accuracy of photometric redshifts (photo-$z$) is essential for reliable statistical studies of cosmology and galaxy evolution. However, missing photometric bands are a common observational challenge that can significantly degrade photo-$z$ estimation accuracy. In this work, we present a systematic evaluation of data imputation methods aimed at improving photo-$z$ performance. We benchmark a range of representative machine learning (ML) and deep learning (DL) architectures, identifying k-nearest neighbors (KNN) and the attention-based SAITS model as the leading performers. These models are then applied to China Space Station Survey Telescope (CSST) mock data to assess their performance under realistic observational conditions. Our results show that KNN yields the highest accuracy under idealized missing completely at random (MCAR) conditions with complete training sets, whereas robustness tests reveal that SAITS significantly outperforms KNN when training data is incomplete or when applied to realistic mixed-mechanism scenarios. We find that domain consistency between training and testing missingness patterns is a prerequisite for optimal performance, highlighting the risks of domain shift in supervised regression tasks. Furthermore, our analysis demonstrates that while general imputation models are highly effective for MCAR and missing at random (MAR) data, they are detrimental when applied to missing not at random (MNAR) data arising from flux limits, as statistical models fail to capture the physical information inherent in these non-detections. Consequently, we advocate for more sophisticated architectures capable of disentangling stochastic missingness from physical non-detections to address these distinct mechanisms individually.

astro-ph.GA↗

arXiv2026

Interactive State Space Model with Cross-Modal Local Scanning for Depth Super-Resolution

Guided depth super-resolution (GDSR) reconstructs HR depth maps from LR inputs with HR RGB guidance. Existing methods either model each modality independently or rely on computationally expensive attention mechanisms with quadratic complexity, hindering the establishment of efficient and semantically interactive joint representations. In this paper, we observe that feature maps from different modalities exhibit semantic-level correlations during feature extraction. This motivates us to develop a more flexible approach enabling dense, semantically-aware deep interactions between modalities. To this end, we propose a novel GDSR framework centered around the Interactive State Space Model. Specifically, we design a cross-modal local scanning mechanism that enables fine-grained semantic interactions between RGB and depth features. Leveraging the Mamba architecture, our framework achieves global modeling with linear complexity. Furthermore, a cross-modal matching transform module is introduced to enhance interactive modeling quality by utilizing representative features from both modalities. Extensive experiments demonstrate competitive performance against state-of-the-art methods.

cs.CV↗

arXiv2026

Constraints Matrix Diffusion based Generative Neural Solver for Vehicle Routing Problems

Over the past decade, neural network solvers powered by generative artificial intelligence have garnered significant attention in the domain of vehicle routing problems (VRPs), owing to their exceptional computational efficiency and superior reasoning capabilities. In particular, autoregressive solvers integrated with reinforcement learning have emerged as a prominent trend. However, much of the existing work emphasizes large-scale generalization of neural approaches while neglecting the limited robustness of attention-based methods across heterogeneous distributions of problem parameters. Their improvements over heuristic search remain largely restricted to hand-curated, fixed-distribution benchmarks. Furthermore, these architectures tend to degrade significantly when node representations are highly similar or when tasks involve long decision horizons. To address the aforementioned limitations, we propose a novel fusion neural network framework that employs a discrete noise graph diffusion model to learn the underlying constraints of vehicle routing problems and generate a constraint assignment matrix. This matrix is subsequently integrated adaptively into the feature representation learning and decision process of the autoregressive solver, serving as a graph structure mask that facilitates the formation of solutions characterized by both global vision and local feature integration. To the best of our knowledge, this work represents the first comprehensive experimental investigation of neural network model solvers across a 378-combinatorial space spanning four distinct dimensions within the CVRPlib public dataset. Extensive experimental evaluations demonstrate that our proposed fusion model effectively captures and leverages problem constraints, achieving state-of-the-art performance across multiple benchmark datasets.

cs.LG↗

arXiv2026

BiM-GeoAttn-Net: Linear-Time Depth Modeling with Geometry-Aware Attention for 3D Aortic Dissection CTA Segmentation

Accurate segmentation of aortic dissection (AD) lumens in CT angiography (CTA) is essential for quantitative morphological assessment and clinical decision-making. However, reliable 3D delineation remains challenging due to limited long-range context modeling, which compromises inter-slice coherence, and insufficient structural discrimination under low-contrast conditions. To address these limitations, we propose BiM-GeoAttn-Net, a lightweight framework that integrates linear-time depth-wise state-space modeling with geometry-aware vessel refinement. Our approach is featured by Bidirectional Depth Mamba (BiM) to efficiently capture cross-slice dependencies and Geometry-Aware Vessel Attention (GeoAttn) module that employs orientation-sensitive anisotropic filtering to refine tubular structures and sharpen ambiguous boundaries. Extensive experiments on a multi-source AD CTA dataset demonstrate that BiM-GeoAttn-Net achieves a Dice score of 93.35% and an HD95 of 12.36 mm, outperforming representative CNN-, Transformer-, and SSM-based baselines in overlap metrics while maintaining competitive boundary accuracy. These results suggest that coupling linear-time depth modeling with geometry-aware refinement provides an effective, computationally efficient solution for robust 3D AD segmentation.

eess.IV↗

arXiv2026

SceneTransporter: Optimal Transport-Guided Compositional Latent Diffusion for Single-Image Structured 3D Scene Generation

We introduce SceneTransporter, an end-to-end framework for structured 3D scene generation from a single image. While existing methods generate part-level 3D objects, they often fail to organize these parts into distinct instances in open-world scenes. Through a debiased clustering probe, we reveal a critical insight: this failure stems from the lack of structural constraints within the model's internal assignment mechanism. Based on this finding, we reframe the task of structured 3D scene generation as a global correlation assignment problem. To solve this, SceneTransporter formulates and solves an entropic Optimal Transport (OT) objective within the denoising loop of the compositional DiT model. This formulation imposes two powerful structural constraints. First, the resulting transport plan gates cross-attention to enforce an exclusive, one-to-one routing of image patches to part-level 3D latents, preventing entanglement. Second, the competitive nature of the transport encourages the grouping of similar patches, a process that is further regularized by an edge-based cost, to form coherent objects and prevent fragmentation. Extensive experiments show that SceneTransporter outperforms existing methods on open-world scene generation, significantly improving instance-level coherence and geometric fidelity. Code and models will be publicly available at https://2019epwl.github.io/SceneTransporter/.

cs.CV↗

arXiv2026

Scan Clusters, Not Pixels: A Cluster-Centric Paradigm for Efficient Ultra-high-definition Image Restoration

Ultra-High-Definition (UHD) image restoration is trapped in a scalability crisis: existing models, bound to pixel-wise operations, demand unsustainable computation. While state space models (SSMs) like Mamba promise linear complexity, their pixel-serial scanning remains a fundamental bottleneck for the millions of pixels in UHD content. We ask: must we process every pixel to understand the image? This paper introduces C$^2$SSM, a visual state space model that breaks this taboo by shifting from pixel-serial to cluster-serial scanning. Our core discovery is that the rich feature distribution of a UHD image can be distilled into a sparse set of semantic centroids via a neural-parameterized mixture model. C$^2$SSM leverages this to reformulate global modeling into a novel dual-path process: it scans and reasons over a handful of cluster centers, then diffuses the global context back to all pixels through a principled similarity distribution, all while a lightweight modulator preserves fine details. This cluster-centric paradigm achieves a decisive leap in efficiency, slashing computational costs while establishing new state-of-the-art results across five UHD restoration tasks. More than a solution, C$^2$SSM charts a new course for efficient large-scale vision: scan clusters, not pixels.

cs.CV↗

arXiv2026

Augmenting Clinical Decision-Making with an Interactive and Interpretable AI Copilot: A Real-World User Study with Clinicians in Nephrology and Obstetrics

Clinician skepticism toward opaque AI hinders adoption in high-stakes healthcare. We present AICare, an interactive and interpretable AI copilot for collaborative clinical decision-making. By analyzing longitudinal electronic health records, AICare grounds dynamic risk predictions in scrutable visualizations and LLM-driven diagnostic recommendations. Through a within-subjects counterbalanced study with 16 clinicians across nephrology and obstetrics, we comprehensively evaluated AICare using objective measures (task completion time and error rate), subjective assessments (NASA-TLX, SUS, and confidence ratings), and semi-structured interviews. Our findings indicate AICare's reduced cognitive workload. Beyond performance metrics, qualitative analysis reveals that trust is actively constructed through verification, with interaction strategies diverging by expertise: junior clinicians used the system as cognitive scaffolding to structure their analysis, while experts engaged in adversarial verification to challenge the AI's logic. This work offers design implications for creating AI systems that function as transparent partners, accommodating diverse reasoning styles to augment rather than replace clinical judgment.

cs.HC↗

arXiv2025

From Events to Clarity: The Event-Guided Diffusion Framework for Dehazing

Clear imaging under hazy conditions is a critical task. Prior-based and neural methods have improved results. However, they operate on RGB frames, which suffer from limited dynamic range. Therefore, dehazing remains ill-posed and can erase structure and illumination details. To address this, we use event cameras for dehazing for the \textbf{first time}. Event cameras offer much higher HDR ($120 dBvs.60 dB$) and microsecond latency, therefore they suit hazy scenes. In practice, transferring HDR cues from events to frames is hard because real paired data are scarce. To tackle this, we propose an event-guided diffusion model that utilizes the strong generative priors of diffusion models to reconstruct clear images from hazy inputs by effectively transferring HDR information from events. Specifically, we design an event-guided module that maps sparse HDR event features, \textit{e.g.,} edges, corners, into the diffusion latent space. This clear conditioning provides precise structural guidance during generation, improves visual realism, and reduces semantic drift. For real-world evaluation, we collect a drone dataset in heavy haze (AQI = 341) with synchronized RGB and event sensors. Experiments on two benchmarks and our dataset achieve state-of-the-art results.

cs.CV↗

arXiv2025

Local potential and H\"older estimates for the linearized Monge-Amp\`ere equation

In this paper, we establish local potential estimates and H\"older estimates for solutions of linearized Monge-Amp\`ere equations with the right-hand side being a signed measure, under suitable assumptions on the data. In particular, the interior H\"older estimate holds for an inhomogeneous linearized Monge-Amp\`ere equation with right-hand side being the nonnegative divergence of a bounded vector field in all dimensions. As an application, we give a new approach for the interior estimate of the singular Abreu equation.

math.AP↗

arXiv2025

TeleEgo: Benchmarking Egocentric AI Assistants in the Wild

Egocentric AI assistants in real-world settings must process multi-modal inputs (video, audio, text), respond in real time, and retain evolving long-term memory. However, existing benchmarks typically evaluate these abilities in isolation, lack realistic streaming scenarios, or support only short-term tasks. We introduce \textbf{TeleEgo}, a long-duration, streaming, omni-modal benchmark for evaluating egocentric AI assistants in realistic daily contexts. The dataset features over 14 hours per participant of synchronized egocentric video, audio, and text across four domains: work \& study, lifestyle \& routines, social activities, and outings \& culture. All data is aligned on a unified global timeline and includes high-quality visual narrations and speech transcripts, curated through human refinement.TeleEgo defines 12 diagnostic subtasks across three core capabilities: Memory (recalling past events), Understanding (interpreting the current moment), and Cross-Memory Reasoning (linking distant events). It contains 3,291 human-verified QA items spanning multiple question formats (single-choice, binary, multi-choice, and open-ended), evaluated strictly in a streaming setting. We propose Real-Time Accuracy (RTA) to jointly capture correctness and responsiveness under tight decision windows, and Memory Persistence Time (MPT) as a forward-looking metric for long-term retention in continuous streams. In this work, we report RTA results for current models and release TeleEgo, together with an MPT evaluation framework, as a realistic and extensible benchmark for future egocentric assistants with stronger streaming memory, enabling systematic study of both real-time behavior and long-horizon memory.

cs.CV↗