arXiv subjects

Long Li

Publications and source records attributed to Long Li.

At least 19 recordsLinked to original sources

arXiv2026

Eigenvalue Asymptotics in High-Contrast Media

We investigate the eigenfrequency asymptotics of a bounded acoustic cavity containing a shrinking high-contrast inclusion. This configuration is motivated by contrast-enhanced ultrasound imaging, in which microbubbles are employed as acoustic contrast agents. We identify dimension-dependent material scalings that keep the inclusion-induced resonance in a fixed order-one frequency regime as the inclusion shrinks. Our main result gives a complete asymptotic description of the spectrum in any prescribed bounded frequency window. Two distinct spectral mechanisms arise: the background Dirichlet eigenfrequencies persist as perturbed eigenvalue clusters, while the singular material contrast creates an additional Minnaert eigenvalue branch. The limiting Minnaert frequency is explicit in both dimensions, with a capacitance-based expression in three dimensions and an area-based expression in two dimensions. Two-dimensional numerical experiments confirm both the perturbation of the background Dirichlet eigenfrequencies and the emergence of the additional Minnaert branch.

math.SP↗

arXiv2026

Simulating passive scalar advection in rough Kraichnan flows

We present a systematic Eulerian study of passive scalar advection in rough two-dimensional Kraichnan flows, covering the full range of velocity roughness exponent $h\in(0,1)$. The advection--diffusion equation is integrated directly using a pseudo-spectral method at resolutions up to $2048^2$ grid points, with a frozen-noise Runge--Kutta scheme consistent with the white-in-time construction of the carrier flow. The simulations recover the duality between advected scalar and advecting flow---the smoother the carrier, the rougher the scalar---together with the predicted scaling laws for the second-order statistics. Once the scaling range is properly identified, the fourth-order flatness anomaly is measured across the whole range of $h$, in agreement with the Lagrangian estimates of Frisch \textit{et al.} (1999) and with the perturbative predictions of Bernard \textit{et al.} (1998) and Pumir \textit{et al.} (1997). Benefiting from the fact that our Eulerian simulations give direct access to the full scalar field, we also examine the probability density functions of scalar increments and the corresponding higher-order statistics, which show systematic departures from Gaussianity and from log-normality, with the strongest deviations manifesting for intermediate values of $h$. A central outcome of this work is a systematic account of how the simulation parameters, in particular the molecular diffusivity, must be adjusted with $h$, providing practical guidelines for reliable simulations; we further show that the residual deviations from the theoretical scaling laws are quantitatively accounted for by the finite spectral representation of the carrier flow. Our analysis also serve as a numerical baseline for simulating more realistic extensions of the Kraichnan model, where the carrier flow is coupled with a Gaussian multiplicative chaos and theoretical developments are limited.

math-ph↗

arXiv2026

Almost periodic solutions of the defocusing mKdV equation

We study the Cauchy problem for the defocusing mKdV equation with almost periodic initial data. If the initial data corresponds to a reflectionless Dirac operator which satisfies certain Craig-type conditions on the spectrum, we prove that the Cauchy problem has solution that is almost periodic in spacetime, and that this is the only solution which is locally bounded in a suitable sense. In particular, the result applies to small analytic quasiperiodic initial data with Diophantine frequencies.

math.AP↗

arXiv2026

One-Dimensional Divergence-Type Jacobi Operators Driven by The Doubling Map

We study one-dimensional Jacobi operators of divergence-gradient type on $\ell^2(\mathbb{Z}_{\geq 0})$, with coefficients generated by the doubling map, $a_n(x)=a(2^n x \mathrm{mod} 1)$. For continuous positive sampling functions, we show that the almost-sure essential spectrum is an interval containing the bottom of the spectrum. Under the assumption $a\in C^1(\mathbb{T})$, we prove square-root asymptotics for the integrated density of states and obtain a small-energy expansion for the Lyapunov exponent as $E\to0^+$. The leading term of the Lyapunov exponent is linear and positive precisely under a nondegeneracy condition on the sampling function. In this case, we prove a large-deviation estimate for the transfer matrices with an explicit rate depending on $E$. As consequences, we obtain local H\"older continuity of the Lyapunov exponent and the integrated density of states near the bottom of the spectrum, as well as the Anderson localization. Some of these results extend the small-coupling results of Chulaevsky--Spencer and Bourgain--Schlag for Schr\"odinger operators generated by the doubling map to divergence-gradient type operators. The arguments adapt methods from those works, but require uniform control in the small-energy parameter and refined correlation estimates reflecting the divergence-gradient structure.

math.SP↗

arXiv2026

Start Classifying: Categorical Critics for LLM Reinforcement Learning

Proximal Policy Optimization (PPO) for large language models typically trains its critic by mean-squared-error (MSE) regression on scalar value targets. Although scalar MSE is statistically valid for estimating the conditional expected return, sparse binary rewards in reinforcement learning with verifiable rewards (RLVR) make critic optimization and calibration especially consequential: small value errors directly distort the scalar advantages used by PPO. We study whether a classification-based training objective can improve this critic signal. HL-Gauss PPO replaces the scalar MSE head with a categorical predictor over a discretized value support, trained by cross-entropy against smoothed HL-Gauss targets. Its output is decoded to a scalar expectation for standard GAE and PPO; the actor update is therefore unchanged and is not distributional. Across mathematical reasoning, tool-augmented math, and Search-R1, and on both Qwen2.5 and Qwen3 backbones, HL-Gauss PPO consistently improves over strong PPO and DAPO baselines. Controls with one-hot, two-hot, and Bernoulli two-bin critics show that neither a larger output head nor binary classification alone explains the gains. On a common collection of reasoning prefixes, HL-Gauss improves Brier score and calibration error and yields more symmetric, lower-variance advantages. These results position categorical value learning as an effective optimization surrogate for PPO critics in RLVR.

cs.LG↗

arXiv2026

Qwen-UI-Agent Technical Report: Toward Next-Generation Real-World Centric Foundation GUI Agents

GUI agents have the potential to become a general purpose executor over existing digital devices. To advance them toward real-world use, we envision agents that operate reliably on real devices, execute workflows across platforms, combine GUI interaction with CLI execution, complete long-horizon tasks, proactively initiate useful services, and autonomously improve their capabilities with minimal human effort. Guided by this vision, we present Qwen-UI-Agent, a real-world centric foundation GUI agent spanning mobile, computer-use, web, and DeepSearch environments. Qwen-UI-Agent combines diverse sandbox environments with a large-scale real-device mobile runtime. Its unified action space interleaves GUI operations with CLI execution and generates batched actions in a single model turn. An AutoResearch-style data flywheel uses agents to construct tasks and environments, diagnose failures, and plan subsequent iterations. Online RL supports training on trajectories exceeding 100 turns, with over 10,000 concurrent environments accelerating rollout. A lightweight harness layer supports proactive service initiation and stateful workflows across mobile and computer. Across a broad suite of evaluations, Qwen-UI-Agent sets state-of-the-art performance on mobile-use benchmarks while delivering competitive performance on computer- and browser-use tasks against frontier models, including Opus 4.8, Gemini 3.1 Pro, and GPT-5.6 Sol. On mobile use, it achieves 82.1% on MobileWorld, 92.2% on MobileWorld-Real, and 97.5% on AndroidDaily. On computer use, it achieves 79.5% on OSWorld-Verified and a 40.0% partial-progress score on OSWorld-v2. On browser use and GUI grounding, it achieves 73.6% on WebArena and 81.5% on ScreenSpot-Pro, respectively.

cs.AI↗

arXiv2026

A counterexample to the zero-mass conjecture

We construct an explicit negative plurisubharmonic function on the unit polydisk in $\mathbb{C}^n, n\geq 2$ with an isolated singularity at the origin. Its Monge-Amp\`{e}re measure is the Dirac mass at the origin, but its Lelong number vanishes. This gives a negative answer to the zero-mass conjecture of Guedj-Rashkovskii in every complex dimension at least two.

math.CV↗

arXiv2026

R-process nucleosynthesis from magnetar giant flares in neutron star--white dwarf mergers: A unified picture for peculiar long gamma-ray bursts

Peculiar long gamma-ray bursts (GRBs), exemplified by GRBs 211211A and 230307A, exhibit a long-duration multi-component prompt emission, an X-ray plateau in their afterglow, and a kilonova signature. Their origin remains highly debated. In this work, we present a unified picture for these events based on neutron star--white dwarf (NS--WD) mergers involving a pre-merger magnetar and a massive WD. In this picture, tidal disruption of the WD forms a constant-entropy accretion disk. Hyperaccretion from this disk onto the NS during the early accretion phase amplifies its toroidal magnetic field to strengths sufficient to trigger repeated magnetar giant flares (GFs). The main burst (MB) of the prompt emission consists of a ``forest'' of initial spikes from these GFs, while the subsequent magnetic propeller phase generates the extended emission (EE) and naturally explains the observed MB--EE trough. Crucially, the $e^{\pm}$-$\gamma$ fireball associated with each GF initial spike shocks the NS crust, leading to crustal ejection that synthesizes r-process heavy elements via the $\alpha$-rich freeze-out mechanism, thereby resolving the r-process deficit in conventional NS--WD hydrodynamic simulations. The ensemble of such fireballs over the MB duration collectively yields $M_{\rm ej}\gtrsim 10^{-5}-10^{-3}\,M_\odot$ of ejecta, sufficient to power the observed kilonova signature when further boosted by the spin-down of the post-merger magnetar. Meanwhile, the spin-down radiation also powers the X-ray plateau. This tidally disrupted NS--WD merger picture provides a self-consistent framework that unifies the prompt emission, afterglow, kilonova, and r-process nucleosynthesis observed in peculiar long GRBs.

astro-ph.HE↗

arXiv2026

Beyond Entropy: Correctness-Aware Advantage Shaping via Contrastive Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) commonly uses entropy for advantage shaping. However, entropy cannot distinguish useful uncertainty from detrimental confusion, limiting its effectiveness as a correctness signal. We propose Contrastive Policy Optimization (CPO), which uses token-level contrastive disagreement between reference-guided and vanilla generation distributions for correctness-aware advantage shaping. Both theoretical and empirical results show that this disagreement reliably indicates token-level correctness. We further show that On-policy Distillation is a special case of CPO, where the posterior distribution is instantiated by an external teacher model. CPO also resolves the zero-advantage problem. Experiments on in-domain and out-of-domain benchmarks demonstrate that CPO substantially outperforms entropy-based RLVR methods while maintaining strong generalization. Further analysis shows that correct and incorrect responses naturally support exploration and exploitation respectively, and balancing both leads to the best performance.

cs.LG↗

arXiv2026

A Time-Domain Pressure-Interface Model for Gas Bubble Dynamics with Surface Tension: Well-Posedness, Classical Limits, and Resonance Branches

We derive and analyze a time-domain pressure--interface evolution model for a compressible gas bubble in a compressible liquid with surface tension. Starting from the nonlinear two-phase Euler free-boundary problem and linearizing about a spherical Young--Laplace equilibrium, we obtain a coupled bulk--surface hyperbolic system for the liquid pressure, the gas pressure, and the normal displacement of the interface. The time-domain analysis is complicated by the fact that the surface-tension quadratic form is indefinite: the $Y_0^0$ component is the volume-changing breathing mode, the $Y_1^m (m = \{-1,0,1\})$ components are neutral translations, and only the higher spherical harmonics give a coercive shape-mode energy. We exploit this decomposition. The coercive sector is treated by a $C^0$-semigroup argument, while the breathing mode is analyzed separately by Fourier--Laplace methods. This yields well-posedness for admissible finite-energy data and classical solutions under the natural compatibility conditions. We then justify two limiting descriptions with quantitative error estimates. In an acoustic quasi-static regime, the model reduces to the linearized Rayleigh--Plesset equation for the breathing mode and to the linearized Rayleigh--Lamb equations for the shape modes. In a different regime, it reduces to the frozen-interface acoustic transmission model. Finally, a frequency-domain analysis identifies the corresponding Minnaert, Rayleigh--Lamb, and Fabry--P\'erot-type resonance mechanisms as different components and limits of the same pressure--interface formulation.

math.AP↗

arXiv2026

Evaluating the Feasibility of Inferring Dietary Behavior Change Receptivity from Egocentric Images of Eating Environment

Accurately assessing dietary behavior change receptivity is essential for designing effective just-in-time adaptive interventions (JITAIs) that promote healthier eating habits. However, self-report-based assessment of behavior change receptivity is sparse and delayed, limiting its practical use in continuous monitoring. To explore whether passive sensing may help address this challenge, this study conducts a pilot investigation of inferring participants' self-reported behavior change receptivity from egocentric eating images collected by a wearable camera. We use pilot data obtained from free-living eating episodes using the Automatic Ingestion Monitor v2 (AIM-2). The data included egocentric image sequences captured during eating and paired with responses to questions assessing specific dimensions of behavior change receptivity (awareness, interaction capability, and motivation). To examine whether visual information contained any relevancy to these responses, we evaluated a transfer-learning-assisted framework that combines a pre-trained Contrastive Language-Image Pre-Training (CLIP) vision encoder with a lightweight transformer classifier. The model processes eating episode image sequences to extract potential semantic and temporal cues related to behavior change receptivity. Preliminary experimental results show promising improvements over simple baseline models for behavior change receptivity indicators. These early findings suggest that egocentric eating episode images may contain cues related to dietary behavior change receptivity, and warrant further investigation with larger and more comprehensive datasets.

cs.CV↗

arXiv2026

WGAN based Inverse Design of Active Dual Band FSS with Switchable Transmission

This letter presents a novel design method for switchable dual band transmissive frequency selective surface (FSS). The proposed FSS possesses characteristics of maintaining passband characteristics at high frequencies, while switching from transmission to reflection at low frequencies with pin diodes states altering. Specifically, we propose a crystal growth-based topology generation strategy, and utilize a simplified U-Net Wasserstein GAN (WGAN) neural network model to establish an inverse mapping model from electromagnetic response to structure topology parameters. The trained WGAN achieves training and validation accuracies of 95.59% and 90.84%, while the simplified U-Net attains training and validation accuracies of 98.5% and 94.1%. Using the trained WGAN. The generated structural topologies were validated through full-wave simulations and experimental measurements. The proposed method enhances the design flexibility and overcomes the time- consuming drawbacks of conventional FSS design.

physics.app-ph↗

arXiv2026

SPPO: Sequence-Level PPO for Long-Horizon Reasoning Tasks

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

cs.AI↗

arXiv2026

A Data-Driven Fast Simulation Approach for MAPS-based Detectors and their Optimization

A parametric simulation tool for pixel sensors is presented. A realistic pixel response is simulated purely based on measurement input, without requiring detailed knowledge of the underlying manufacturing process. As such, it provides an efficient alternative to the use of Technology Computer-Aided Design simulations, which typically depend on proprietary process information. Due to its parametric approach, the package is fast and thus particularly useful for larger detector systems and high hit rate environments. This work presents measurements, simulation and its validation for the MALTA2 sensor. It is a small collection electrode monolithic active pixel sensor produced in the Tower 180nm Complementary Metal-Oxide-Semiconductor imaging process. Modifications to the sensor's periphery, mainly in the hit merger, are studied in order to optimize the performance for tracking and calorimetry. This optimization is of special interest as part of the MALTA3 sensor redesign in the 65nm Tower Partners Semiconductor Co. process.

physics.ins-det↗

arXiv2026

Leum-VL Technical Report

A short video succeeds not simply because of what it shows, but because of how it schedules attention -- yet current multimodal models lack the structural grammar to parse or produce this organization. Existing models can describe scenes, answer event-centric questions, and read on-screen text, but they are far less reliable at identifying timeline-grounded units such as hooks, cut rationales, shot-induced tension, and platform-facing packaging cues. We propose SV6D (Structured Video in Six Dimensions), inspired by professional storyboard practice in film and television production, a representation framework that decomposes internet-native video into six complementary structural dimensions -- subject, aesthetics, camera language, editing, narrative, and dissemination -- with each label tied to physically observable evidence on the timeline. We formalize a unified optimization objective over SV6D that combines Hungarian-matched temporal alignment, dimension-wise semantic label distance, and quality regularization. Building on this framework, we present Leum-VL-8B, an 8B video-language model that realizes the SV6D objective through an expert-driven post-training pipeline, further refined through verifiable reinforcement learning on perception-oriented tasks. Leum-VL-8B achieves 70.8 on VideoMME (w/o subtitles), 70.0 on MVBench, and 61.6 on MotionBench, while remaining competitive on general multimodal evaluations such as MMBench-EN. We also construct FeedBench, a benchmark for structure-sensitive short-video understanding. Our results indicate that the missing layer in video AI is not pixel generation but structural representation: grounded on the timeline, linked to visible evidence, and directly consumable by downstream workflows such as editing, retrieval, recommendation, and generation control, including text-heavy internet video formats with overlays and image-text layouts.

cs.MM↗

arXiv2026

DyJR: Preserving Diversity in Reinforcement Learning with Verifiable Rewards via Dynamic Jensen-Shannon Replay

While Reinforcement Learning (RL) enhances Large Language Model reasoning, on-policy algorithms like GRPO are sample-inefficient as they discard past rollouts. Existing experience replay methods address this by reusing accurate samples for direct policy updates, but this often incurs high computational costs and causes mode collapse via overfitting. We argue that historical data should prioritize sustaining diversity rather than simply reinforcing accuracy. To this end, we propose Dynamic Jensen-Shannon Replay (DyJR), a simple yet effective regularization framework using a dynamic reference distribution from recent trajectories. DyJR introduces two innovations: (1) A Time-Sensitive Dynamic Buffer that uses FIFO and adaptive sizing to retain only temporally proximal samples, synchronizing with model evolution; and (2) Jensen-Shannon Divergence Regularization, which replaces direct gradient updates with a distributional constraint to prevent diversity collapse. Experiments on mathematical reasoning and Text-to-SQL benchmarks demonstrate that DyJR significantly outperforms GRPO as well as baselines such as RLEP and Ex-GRPO, while maintaining training efficiency comparable to the original GRPO. Furthermore, from the perspective of Rank-$k$ token probability evolution, we show that DyJR enhances diversity and mitigates over-reliance on Rank-1 tokens, elucidating how specific sub-modules of DyJR influence the training dynamics.

cs.LG↗

arXiv2026

SQL-ASTRA: Alleviating Sparse Feedback in Agentic SQL via Column-Set Matching and Trajectory Aggregation

Agentic Reinforcement Learning (RL) shows promise for complex tasks, but Text-to-SQL remains mostly restricted to single-turn paradigms. A primary bottleneck is the credit assignment problem. In traditional paradigms, rewards are determined solely by the final-turn feedback, which ignores the intermediate process and leads to ambiguous credit evaluation. To address this, we propose Agentic SQL, a framework featuring a universal two-tiered reward mechanism designed to provide effective trajectory-level evaluation and dense step-level signals. First, we introduce Aggregated Trajectory Reward (ATR) to resolve multi-turn credit assignment. Using an asymmetric transition matrix, ATR aggregates process-oriented scores to incentivize continuous improvement. Leveraging Lyapunov stability theory, we prove ATR acts as an energy dissipation operator, guaranteeing a cycle-free policy and monotonic convergence. Second, Column-Set Matching Reward (CSMR) provides immediate step-level rewards to mitigate sparsity. By executing queries at each turn, CSMR converts binary (0/1) feedback into dense [0, 1] signals based on partial correctness. Evaluations on BIRD show a 5% gain over binary-reward GRPO. Notably, our approach outperforms SOTA Arctic-Text2SQL-R1-7B on BIRD and Spider 2.0 using identical models, propelling Text-to-SQL toward a robust multi-turn agent paradigm.

cs.AI↗

arXiv2026

AT 2024wpp: the most luminous fast-evolving optical transient linked to the merger explosion of a black-hole binary

Fast blue optical transients (FBOTs) represent one of the most exotic astrophysical transients, exhibiting unusually strong emission across X-ray, optical, and radio wavelengths. Their physical origins remain highly debated, with proposed explanations ranging from stellar explosion to tidal disruption event (TDE). Here we report observations of the most luminous FBOT, AT 2024wpp whose post-peak luminosity rebrightens in X ray and becomes flattening in optical in a manner follows the decay rate characteristic of TDEs ($L_{\rm bol} \propto t^{-5/3}$). This invokes energy contribution of accretion by a central compact object, getting further corroborations from hardening of X-ray spectral index and detection of outflow inferred from the emission lines at similar phase. Detailed modeling of luminsoity evolution favors a coalesce explosion of a 34 M$_{\odot}$ Wolf-Rayet star with a 15 M$_{\odot}$ black hole (BH), demonstrating that some FBOTs may be associated with TDE of a stellar blackhole.

astro-ph.HE↗