arXiv subjects

Ke Wang

Publications and source records attributed to Ke Wang.

At least 19 recordsLinked to original sources

arXiv2026

Word Length Formulae, Normal Forms, Conjugation and Root-finding Algorithms in Surface Groups

In this paper, we mainly study the following symmetric presentation of the surface group $$π_1(Σ_g)=\left\langle c_1,\dots, c_{2g}\mid c_1\cdots c_{2g}c_1^{-1}\cdots c_{2g}^{-1}\right\rangle.$$ For every nontrivial element $x\in π_1(Σ_g)$ and $k\geq 2$, we obtain a uniform representative of the normal forms $\mathfrak{nf}(x^k)$ of $x^k$ under the length-lexicographical order: $$\mathfrak{nf}(x^k) = \overline{LW^{k-2}R}.$$ Building on this result, we establish a new relation among these normal forms, and then derive the following three formulae related to the word length: $|x^2|>|x|$; $|x^k|=(k-1)(|x^2|-|x|)+|x|$; $\lim_{k\to\infty}\frac{|x^k|}{k}=|x^2|-|x|$. Furthermore, we extend these results to obtain a coarser analogue for every minimal geometric presentation. We then define normal forms of conjugacy classes in $π_1(Σ_g)$ and provide a criterion for determining the conjugacy of group elements. As a consequence, we provide efficient algorithms for solving the root-finding and conjugacy problems. Finally, we present applications to the computation of several growth rates.

math.GT↗

arXiv2026

Beyond Lindblad Approximation: Rigorous Guarantees for Thermal and Ground State Preservation under System-Bath Interactions

We establish rigorous guarantees for quantum thermal and ground state preparation via system-bath interactions beyond the Lindblad approximation regime. In contrast to existing analyses, we show that the system-bath coupling strength need not vanish with the target accuracy: even when the coupling strength is chosen independently of the desired precision, the induced quantum channel admits the target thermal and ground states as approximate fixed points with arbitrarily small error. Our analysis develops new techniques to control all orders of the Dyson expansion and the associated multidimensional operator Fourier transforms, thereby going beyond the leading-order Lindbladian description. Building on these estimates, we derive an improved end-to-end complexity analysis and provide rigorous guarantees for thermalization and cooling outside the conventional Lindblad approximation regime. Numerical simulations further demonstrate the robustness of the system-bath interaction framework over a broad range of coupling strengths, including regimes where the Lindblad approximation is no longer accurate.

quant-ph↗

arXiv2026

Measuring vacancy-type defect density in monolayer semiconductors

Two-dimensional (2D) materials have attracted wide-spread interest due to their unique and tunable properties. Their optoelectronic, mechanical, and thermal properties are greatly influenced by crystal defects, which are, in turn, used to control these properties. However, experimental quantification of the density of defects, whether deliberately introduced or inherent, is very difficult in these atomically thin materials. Here we show that helium atom micro-diffraction can be used to measure the defect density in ~15x20um monolayer MoS2, a prototypical 2D semiconductor, quickly and easily compared to standard methods. We present a simple analytic model, the lattice gas equation, that captures the relationship between atomic Bragg diffraction intensity and defect density. The model, combined with ab initio scattering calculations, shows that our technique can immediately be applied to a wide range of 2D materials, independent of sample chemistry or structure. Additionally, wafer-scale characterization is immediately possible.

physics.app-ph↗

arXiv2026

Hindsight-Anchored Policy Optimization: Learning Through Hindsight with Thompson Sampling-Inspired Adaptive Gating

Reinforcement Learning with Verifiable Rewards improves reasoning in large language models, yet on-policy learning often suffers from cold-start challenges in sparse-reward settings. Recent mixed-policy approaches address this by combining off-policy teacher data with on-policy training. However, simply combining these introduce a persistent off-policy gradient mass that risks training collapse and instability. To address this challenge, we propose Hindsight-Anchored Policy Optimization (HAPO), a framework that allows teacher intervention to act as a temporary support. HAPO employs Beta-Binomial confidence gating, an adaptive gating mechanism that decides when to open the gate for teacher intervention. The intervention operates with Synthetic Success Injection, which replaces the group's lowest-reward rollout with a verified teacher trajectory. We also introduce adaptive threshold annealing, which gradually retracts the support and restores on-policy training within a finite horizon to mitigate persistent off-policy drift. We demonstrate that HAPO can be layered on top of existing mixed-policy methods in a generalizable manner. Across six math reasoning benchmarks and two model scales, HAPO improves the average accuracy of three major mixed-policy methods while maintaining training stability.

cs.LG↗

arXiv2026

Cognitive Link-Flexible FTN-OTFS Design for High-Mobility LEO Satellite Communications

Low Earth orbit (LEO) satellite links are challenged by pronounced signal-to-noise ratio (SNR) variation and severe Doppler shifts. Although mobility robustness is provided by orthogonal time frequency space (OTFS) modulation, the rate-reliability tradeoff of faster-than-Nyquist (FTN) signaling is constrained by fixed packing. In this paper, an SNR-aware flexible FTN-OTFS framework is proposed, in which the packing factor is adapted to changing link conditions under a prescribed reliability requirement. Link-state perception and packing decisions are supported by estimated SNR and offline reliability thresholds, with constant decision complexity achieved through a fixed-mode lookup table. Elevation-dependent propagation, fractional Doppler, and FTN-induced interference are incorporated into the signal model, while colored noise is accommodated by covariance-aware linear minimum mean-square error detection. Throughput and bit error rate are analytically characterized, and energy efficiency and peak-to-average power ratio are evaluated. Simulation results show that conservative packing preserves reliability under unfavorable conditions, while denser signaling improves throughput as the link strengthens. These findings highlight the potential of cognitive FTN adaptation for efficient future LEO wireless communications.

cs.IT↗

arXiv2026

Decoupling Error Attribution in Cloud-Native Graph-RAG: A Data Integrity Diagnostic Framework

Graph-RAG systems often assume pristine data quality, overlooking the severe impact of perturbations in cloud-native databases. This paper proposes a three-layer decoupled diagnostic framework to orthogonally attribute system errors to reasoning loss, Knowledge Graph (KG) defects, and Cypher generation errors. Evaluated on a spatio-temporal ecological KG of the Southeastern Tibet region with eight defect types, results reveal that data integrity, rather than algorithmic reasoning, is the dominant performance bottleneck, with structural defects degrading system accuracy from 0.93 to 0.39. Crucially, we observe a masking-like phenomenon termed the Parametric Knowledge Masking Effect (PKME), suggesting LLMs compensate for broken retrieval paths using internal memory. This shrinks apparent query generation errors by over 70 percent, obscuring actual storage deterioration and increasing the risk of false negatives for automated monitoring. This work provides a quantitative foundation for auditing and optimizing data integrity in cloud-based information fusion systems.

cs.IR↗

arXiv2026

Electrodynamic Signatures of Bogoliubov Fermi Surfaces in Moiré Graphene

Understanding the superfluid stiffness $D_s$ is a central problem in flat-band superconductivity. It is often interpreted together with spectroscopic probes such as tunneling, since both ultimately reflect the same superconducting quasiparticles. Their relationship is nevertheless complicated in flat bands, where quantum-geometric contributions to $D_s$ must be included. The situation in moiré graphene is particularly complex: tunneling experiments in some cases reveal an evolution between V- and U-shaped spectra together with a quite universal finite zero-bias conductance (ZBC). These two phenomena along with others have been argued to suggest the presence of a Bogoliubov Fermi surface (BFS), often generated by finite-momentum pair-density-wave (PDW) superconductivity. In this paper we calculate the superfluid stiffness in the presence of such a PDW. Virtual interband processes provide the familiar positive geometric contribution that gives phase rigidity to the flat-band condensate, allowing superconductivity to survive even in the presence of a BFS. At the same time, the multiband PDW pair structure enables the gapless BFS quasiparticles to respond to a phase gradient despite the negligible ordinary flat-band velocity. Their resulting counterflow reduces the stiffness even at zero temperature. As an experimentally accessible consequence, we predict a correlated evolution of the residual ZBC and the low-temperature stiffness: enhanced zero-bias spectral weight should accompany reduced phase rigidity. Observation of this correlation would support the presence of a BFS and indicate that the residual zero-energy states are intrinsic.

cond-mat.supr-con↗

arXiv2026

A Self-Adaptive First-Principles Approach for Magnetic Excited States

The profound impact of excited magnetic states on the intricate interplay between electron and lattice behaviors in magnetic materials is a topic of great interest. Unfortunately, despite the significant strides that have been made in first-principles methods, accurately tracking these phenomena remains a challenging and elusive task. The crux of the challenge that lies before us is centered on the intricate task of characterizing the magnetic configuration of an excited state, utilizing a first-principle approach that is firmly rooted in the ground state of the system. We propose a versatile self-adaptive spin-constrained density functional theory formalism. By iteratively optimizing the constraining field alongside the electron wave function during energy minimization, we are able to obtain an accurate potential energy surface that captures the longitudinal and transverse variations of magnetization in itinerant ferromagnetic Fe. Moreover, this technique allows us to identify the subtle coupling between magnetic moments and other degrees of freedom by tracking energy variation, providing new insights into the intricate interplay between magnetic interactions, electronic band structure, and phonon dispersion curves in single-layered CrI$_3$. This new methodology represents a significant breakthrough in our ability to probe the complex and multifaceted properties of magnetic systems.

cond-mat.mtrl-sci↗

arXiv2026

Enhancing Multimodal Emotion Recognition via Multi-Feature Encoding and Attention-Based Fusion

Multimodal emotion recognition has attracted growing interest due to its importance in human-computer interaction, remote education, and healthcare. This paper proposes a novel multimodal emotion recognition framework that integrates rich audio and visual feature extraction with an attention-based fusion strategy. For audio, we extract three complementary feature types: semantic embeddings from Wav2Vec2, MFCC features, and statistical acoustic descriptors such as pitch, energy, and rhythm. These are aligned and fused via a BiLSTM to capture temporal dependencies. For video, we propose a ResNet50-BiLSTM architecture that combines deep residual learning and sequential modeling to extract expressive spatiotemporal features from facial sequences. To enhance multimodal synergy, we introduce a feature-level fusion mechanism based on multi-head attention, allowing the model to adaptively weigh contributions across modalities. Experiments conducted on the MELD and IEMOCAP datasets demonstrate that our model significantly outperforms baselines in both accuracy and robustness. Furthermore, ablation studies show that the attention-based fusion strategy significantly improves performance in unbalanced data settings. Our findings suggest that the proposed framework effectively captures diverse emotional cues from speech and visual expressions, and offers a practical and generalizable approach for real-world multimodal emotion recognition tasks.

cs.CV↗

arXiv2026

OPUS-V2: Bridging the Gap between Sparse Points and Dense Voxels

The point-based occupancy prediction paradigm has achieved an attractive trade-off between accuracy and efficiency by modeling 3D space sparsely. However, its predictions inherently mismatch the dense voxel-based occupancy required by self-driving systems, necessitating hand-crafted heuristics during training and inference that limit final performance. To overcome these limitations, we propose OPUS-V2, a novel framework built upon the pioneering OPUS (occupancy prediction using a sparse set) point-based approach. OPUS-V2 incorporates a lightweight point-voxel transformation (PVT) module behind the decoder to adaptively map sparse predictions into the dense voxel space, eliminating the need for suboptimal operations and improving model accuracy. Furthermore, our architecture decouples feature and occupancy generation processes, allowing OPUS-V2 to adapt to arbitrary occupancy resolutions. OPUS-V2 achieves a state-of-the-art rayIoU of 44.0 on the Occ3D dataset. On the more challenging OpenOccupancy dataset, it attains a competitive 16.4 mIoU while running in real time at 20.6 FPS.

cs.CV↗

arXiv2026

Dense Cores in the Vicinity of an HII Region

Massive stars strongly influence their surroundings through radiative and mechanical feedback, but its effects on dense gas structures at sub-pc scales remain poorly constrained. We investigate how feedback from a newly formed massive star affects dense cores in the filamentary molecular cloud IRAS 18530+0215. We analyze ALMA Band 6 observations of 1.3 mm dust continuum and DCN, N$_2$D$^+$, and $^{13}$CS line emission, together with VLA K-band continuum and NH$_3$ observations. Dense cores are identified with astrodendro, and their temperatures, masses, velocity dispersions, and virial parameters are derived. The dynamical state of the ultra-compact H II region is examined through energy and pressure estimates. The H II region has a radius of $\sim$0.1 pc and an expansion velocity of $\sim$2.5 km s$^{-1}$, corresponding to a shell dynamical age of $\sim$0.06 Myr. DCN and $^{13}$CS cores are concentrated near the H II region, whereas N$_2$D$^+$ cores preferentially lie farther away. Core temperatures and velocity dispersions decrease with projected distance from the H II region. Virial parameters increase within the inner $\sim$0.3 pc but decline sharply beyond this scale, while core masses show no significant trend with distance. Strong star formation signatures are found at $\sim$0.2 pc, whereas more distant regions still host quiescent, cold dense cores. The compact H II region appears trapped or choked within $\sim$0.1 pc, while its feedback extends to at least $\sim$0.3 pc. Within this region, feedback enhances core velocity dispersions, gas temperatures, and virial parameters, with no evidence that it promotes the formation of more massive dense cores.

astro-ph.GA↗

arXiv2026

Three omitted values and non-Blaschke point divisors in half-planes

We construct a real meromorphic function $F$ on $\mathbb C$ such that $F^{-1}(\{0,1,\infty\})\subset\mathbb R$, while $F$ is not of bounded type in either half-plane. More strongly, for every $a\in\widehat{\mathbb C}\setminus\{0,1,\infty\}$, the $a$-point divisor in either half-plane fails the Blaschke condition. Thus the construction provides an independent negative answer to a question going back to Nevanlinna's 1925 work that had remained open for over a century. Postcomposition gives the analogous counterexample for any prescribed triple of distinct values in the Riemann sphere. The core construction and proof were generated during an autonomous run of GPT-5.6 Sol Ultra.

math.CV↗

arXiv2026

Geometric bias in eigenspace perturbation under random heterogeneous noise

Spectral methods rely on the stability of principal eigenspaces under random perturbations. Classically, this is quantified by the Davis-Kahan and Wedin theorems, which bound the eigenspace error via the operator norm of the noise and the relevant spectral gaps. While sharp for arbitrary deterministic perturbations, these worst-case bounds can be wasteful in the low-rank signal-plus-noise setting, as they fail to capture the interaction between the signal geometry and the noise distribution. We study the spectral perturbation of signal-plus-noise matrices corrupted by sparse random noise with an arbitrary, inhomogeneous variance profile. Under heterogeneous variances, the empirical eigenvectors suffer a systematic, deterministic geometric bias invisible to classical bounds. Leveraging the Quadratic Vector Equation (QVE) and fine-grained isotropic local laws, we derive near-optimal, non-asymptotic bounds for the leading eigenspaces in the operator and 2-to-infinity norms. These separate the usual signal-to-noise contribution, stochastic fluctuations, and structured geometric bias terms determined by the alignment between the signal eigenspaces and the row-wise variance profile. We further develop refined rowwise bounds that adapt to the variance-weighted leverage of the signal space, yielding sharper guarantees in delocalized regimes. As applications, we establish strong consistency of adjacency spectral clustering for degree-corrected stochastic block models with heterogeneous degrees and unbalanced communities, recovering the logarithmic expected-degree scale in the regular balanced case. We also study spectral embedding for generalized random dot product graphs, showing that the full signal embedding admits sharp rowwise control, whereas spectral truncation can retain a systematic geometric bias determined by the omitted signal directions and the variance profile.

math.ST↗

arXiv2026

Deep Contrastive Unlearning for Language Models

The past a few years have witnessed the great success of large language models, demonstrating powerful capabilities in comprehending textual data and generating human-like languages. Large language models achieve success by being trained on vast amounts of textual data, including online sources with copyrighted content and user-generated knowledge. However, this comes at a cost: the potential risk of exposing users' privacy and violating copyright protections. Thus, to safeguard individuals' "right to be forgotten", there has been increasing interests in machine unlearning -- the process of removing information carried by particular training samples from a model while not deteriorating its predictive quality. This is a challenging task due to the black-box nature of language models. Most existing studies focus on mitigating the impact of those forgot samples upon a model's outputs, and do not explicitly consider the geometric distributions of samples in the latent space of a model. To address this issue, we propose a machine unlearning framework, named Deep Contrastive Unlearning for fine-Tuning (DeepCUT) language models. Our proposed model achieves machine unlearning by directly optimizing the latent space of a model. Comprehensive experiments on real-world datasets demonstrate the effectiveness and efficiency of DeepCUT with consistent and significant improvement over baseline methods.

cs.CL↗

arXiv2026

SlidesGen-Bench: Evaluating Slides Generation via Computational and Quantitative Metrics

The rapid evolution of Large Language Models (LLMs) has fostered diverse paradigms for automated slide generation, ranging from code-driven layouts to image-centric synthesis. However, evaluating these heterogeneous systems remains challenging, as existing protocols often struggle to provide comparable scores across architectures or rely on uncalibrated judgments. In this paper, we introduce SlidesGen-Bench, a benchmark designed to evaluate slide generation through a lens of three core principles: universality, quantification, and reliability. First, to establish a unified evaluation framework, we ground our analysis in the visual domain, treating terminal outputs as renderings to remain agnostic to the underlying generation method. Second, we propose a computational approach that quantitatively assesses slides across three distinct dimensions - Content, Aesthetics, and Editability - offering reproducible metrics where prior works relied on subjective or reference-dependent proxies. Finally, to ensure high correlation with human preference, we construct the Slides-Align1.5k dataset, a human preference aligned dataset covering slides from nine mainstream generation systems across seven scenarios. Our experiments demonstrate that SlidesGen-Bench achieves a higher degree of alignment with human judgment than existing evaluation pipelines. Our code and data are available at https://github.com/YunqiaoYang/SlidesGen-Bench.

cs.CL↗

arXiv2026

OccluRank: Controllable Occlusion-Aware Layout-to-Image Generation by Adding Just an Ordinal Rank

Layout-to-image generation enables explicit spatial control through bounding-box layouts, yet bounding boxes specify only instance locations and cannot represent their occlusion order. Existing methods may rely on additional geometric conditions, employ complex inference procedures, or aggregate independently constructed instance representations without explicitly modeling their occlusion-dependent interactions. We propose OccluRank, a simple and controllable occlusion-aware layout-to-image framework that augments each bounding box with only one ordinal rank. OccluRank encodes the user-specified occlusion order through lightweight rank-based conditioning and introduces an Order-aware Instance Interaction (OII) module to jointly update rank-conditioned instance representations before aggregation. This allows the specified order to guide information exchange among occluding instances without additional geometric inputs or specialized inference-time optimization. We further construct OccluLayout, a synthetic training dataset whose occlusion order and amodal annotations are derived directly from known scene geometry rather than estimated from partially occluded images using auxiliary prediction models. For comprehensive evaluation, we introduce OccluLayout-Bench, which uses multiple multimodal large language model evaluators to assess instance presence, spatial layout, attributes, and occlusion order, together with FID for overall image quality. Experiments show that OccluRank more reliably preserves target instances, follows specified layouts, and realizes desired occlusion relationships while maintaining comparable attribute consistency and overall image quality.

cs.CV↗

arXiv2026

ALOHA IRDCs Molecular Line Follow-up: I. Gas properties and kinematics

Infrared Dark Clouds are ideal sites for investigating the initial conditions of massive star and cluster formation. The A Lei Of the Habitat and Assembly of Infrared Dark Clouds (ALOHA IRDCs), a James Clerk Maxwell Telescope (JCMT) Large Program, has mapped nearby IRDCs with SCUBA-2. Complementary molecular line observations are needed to characterise the physical, kinematic, and chemical properties of the dense gas. We aim to determine the thermal, kinematic, and chemical properties of clumps identified in the ALOHA IRDCs, and to assess their evolutionary status and level of star-forming activity. We performed single-pointing K-band and W-band observations towards 56 ALOHA IRDCs clumps using the Effelsberg 100-m and Yebes 40-m telescopes, respectively. We derived NH3 kinetic temperatures using the hyperfine group ratio (HFGR) method and identified infall and shock signatures from HCO+, H13CO+, SiO, and HNCO profiles. Water masers and NH2D emission were used as complementary tracers of chemical evolution and star formation. The clumps exhibit kinetic temperatures of 15-29 K. We detect NH2D emission towards 18 sources, with NH2D centroid velocities consistent with NH3, indicating both species trace the same dense gas component. More than half of the clumps display blue-asymmetric HCO+ profiles, identifying them as infall candidates. Water masers are detected in 22 sources, with prominent velocity ranges and variability. Broad SiO emission (>~20 km/s) indicates strong shocks, while narrower extents (<~6km/s) likely trace large-scale interactions or low-velocity shocks. The widespread infall signatures, shock tracers, masers, and NH2D emission suggest that relatively quiescent, chemically young material can coexist with dynamically active gas affected by early protostellar feedback, providing insight into the coupled physical and chemical evolution of massive IRDC clumps.

astro-ph.GA↗

arXiv2026

Impact of a Cold Dark Matter Halo on Magnetic Reconnection and Energy Extraction from Kerr-like Black Holes

Recently, Comisso and Asenjo introduced a new energy extraction mechanism based on magnetic reconnection. In this paper, we investigate the power and efficiency of magnetic reconnection energy extraction in a rotating black hole surrounded by a cold dark matter halo. We first examine the properties of the underlying spacetime and its physical quantities, including the event horizon, photon sphere, and ergosphere. We then analyze the allowed energy extraction region and the corresponding energy extraction efficiency for circular orbits. Our results show that energy extraction is feasible for black holes with a spin parameter.

gr-qc↗