Papers

We present a robust deep generative framework for unsupervised image prototype discovery, built on a heavy-tailed Student's t mixture prior, that bridges statistical robustness and mathematical tractability. Existing generative approaches typically rely on noise-prone Gaussian priors or computationally intensive diffusion models; neither simultaneously provides explicit latent structure nor exact analytic optimization. While diffusion models can yield strong priors, iterative sampling and intractable likelihoods limit scalability and interpretability for prototype discovery. We address these issues by constructing a Student's t latent space via a Bayesian scale-mixture formulation. This yields a fully closed-form augmented ELBO for unsupervised Student's t mixture variational autoencoders, which, to our knowledge, is the first such objective applied to robust image prototype discovery, avoiding biased variational approximations and high computational costs in prior heavy-tailed or diffusion-based frameworks. Treating precision as a latent variable automatically modulates each data point's influence, downweighting outliers to learn a data-dependent measure of trust. The result is improved robustness, accuracy, and efficiency, with well-separated latent representations and more stable manifold learning than state-of-the-art methods. We validate our model on standard vision benchmarks and challenging neuroimaging tasks. In brain MRI-driven neurodegenerative disease analysis, our model recovers clean, anatomically coherent prototypes where clinical noise often collapses rare subtypes. These results highlight the ability of our framework to preserve anatomy-associated patterns for precise discovery in clinical settings. Our code is available at: https://github.com/xuzhikangnba/torch-tvae.

We study how many bits are needed to write down an elementary analytic expression that uniformly approximates a Lipschitz function. Expressions are finite trees over the basis $\{+,-,\times,\div,\exp\}$ with the variables and rational constants, and their size is $\dc(f)$, the length of the shortest description of $f$ in a fixed binary description language. For functions of one variable we prove that every $L$-Lipschitz $F:[0,1]\to[0,1]$ has an everywhere-defined approximant of accuracy $\Delta$ with $\dc(f)\le C\,(L/\Delta+\lg(1/\Delta+2))$ for all $L,\Delta>0$, by a linear spline smoothed with logistic ramps in a description language with one repetition construct. We prove a matching lower bound valid for every description language: for $\Delta\le 1/36$ and every $L>0$ some $L$-Lipschitz function needs at least $\tfrac1{16}(L/\Delta+\lg(1/\Delta+2))$ bits. Hence the worst-case description complexity is $\Theta(L/\Delta+\lg(1/\Delta+2))$. For functions on $[0,1]^d$ the same method gives $\Theta_d\bigl((L/\Delta)^d+\lg(1/\Delta+2)\bigr)$, using a tensor-product spline whose coefficients are mixed second differences and cost $O(d)$ bits each. Without the repetition construct the upper bounds carry an additional logarithmic factor, whose necessity for plain expression trees is left open. A reference encoder, decoder and evaluator confirm the constructions numerically, and figures and tables report the checks.

Let $G$ be a finite bipartite graph and let $\widetilde G$ be an $M$-fold cover. We compare independent sets of $\widetilde G$ with those of the trivial cover, consisting of $M$ disjoint copies of $G$, after prescribing how many vertices are selected above each vertex of $G$. A conjecture from 2011, motivated by the Bethe approximation, asserts that the trivial cover maximizes every such count. We prove this for every feasible occupation profile whose active graph has treewidth at most two or is chordal bipartite. Equality holds exactly when the restricted cover is flat, meaning that fibre relabelings make it trivial. For $M\ge2$ and positive feasible occupations, a nonflat cover of a connected bipartite graph of treewidth at most two has a deficit of at least twice the coefficient of $p_G^{M-2}$ with every occupation reduced by one. A holonomy-dependent bound improves the factor to three for odd-order holonomy; both uniform constants are sharp. Comparison and rigidity survive finite compositions along an edge or a vertex, and quantitative bounds from one piece propagate to the whole graph, giving results beyond the two original classes. On any bipartite base, the first nonzero homogeneous defect is determined by the shortest cycles with nontrivial holonomy. At singleton occupations, our counts are numbers of DP-colorings of full covers. The dual DP color function on these classes and their finite seam compositions equals the chromatic polynomial, with equality attained precisely by canonical labelings. Dong's chromatic-polynomial inequality then yields the Dual-DP Shameful inequality on the same graph class. The main theorems have been formalized in Lean 4.

Universal machine-learning interatomic potentials hold the promise to replace costly ab initio calculations in materials science workflows. However, the accuracy and transferability of current models are limited by the availability of training data. We release WBM-MatPES, a dataset of 182 thousand structures recomputed with consistent MatPES settings, together with two reference convex hulls of different depths and test sets at six pressures up to 150 GPa. These datasets reproduce a realistic discovery workflow and allow potentials to be ranked systematically at this level of theory, similar to the Matbench Discovery leaderboard at the Materials Project settings. In this benchmark, five published MatPES potentials agree within 12 meV/atom at 25 GPa, yet their errors increase dramatically to 0.4-5 eV/atom at 150 GPa. To address this limitation, we develop Tuga-FF, a graph transformer trained on datasets spanning ambient and high-pressure configurations alike. Tuga-FF is the most accurate model in the benchmark at ambient pressure, with an energy error of 13.6 meV/atom, and maintains an error of just 21 meV/atom at 150 GPa. We believe this benchmark will encourage the community to train higher-accuracy models and generate richer datasets, advancing machine-learned interatomic potentials as a whole.

This paper presents wideband indoor channel measurements and measurement-based statistical modeling of channel parameters in the upper 6 GHz (U6G) band using directional and quasi-omnidirectional antenna pairs. Measurements span 6.425-7.125 GHz at 32 matched positions per configuration in an open hall and an L-shaped corridor. System calibration and frequency-dependent peak-gain normalization retain antenna radiation-pattern weighting. Close-in and floating-intercept models are fitted to line-of-sight (LOS) and non-LOS (NLOS) path loss, respectively. Shadow-fading residuals, RMS delay spread (DS), and equivalent K factors derived from power delay profiles are characterized. LOS exponents range from 1.98 to 2.14. Despite similar attenuation slopes, directional links exhibit smaller LOS residuals and DS and higher equivalent K factors. Hall DS medians are 1.78 and 36.52 ns for directional and quasi-omnidirectional links. Corridor NLOS slopes are -1.12 and 2.54, respectively, while DS ordering varies by position. These results characterize antenna-dependent parameters for U6G indoor channels.

Bilateral teleoperation with force feedback is becoming increasingly important, and the quality of external-torque estimation is critical to this process. However, manufacturer-provided disturbance-torque estimates on commercial robotic arms are often inaccurate, while the use of end-effector force/torque sensors adds cost and payload. We propose LETS, a physics-guided learning approach that assigns rigid-body dynamics to recursive Newton-Euler inverse dynamics and reserves learning for only the robot-specific residual. LETS uses only the robot's URDF model and joint feedback, deliberately excluding control commands and thereby decoupling external-torque estimation from control-command inputs. It trains on 12 minutes of free-motion data in under one minute, without requiring a dedicated end-effector six-axis force/torque sensor. In bilateral teleoperation, LETS achieves real-time external-torque estimation that enables stable force feedback. Its free-space error is 69% lower than the manufacturer-provided estimate, substantially reducing coupled oscillations between leader and follower; its contact error is 28% lower, yielding more accurate haptic feedback.

We establish the holomorphic dependence of the Helmholtz Calderón projector on closed $C^{1,1}$ surfaces and of the operator associated with the Maxwell electric field integral equation (EFIE) on closed and open surfaces of the same regularity. More precisely, after transporting the boundary integral operators (BIOs) to fixed reference spaces, we prove that the resulting maps admit bounded holomorphic extensions to complex neighborhoods of compact sets of admissible boundary transformations, a property referred to as shape holomorphy. A key step in our proof consists in extending the results in [Lanza de Cristoforis and Rossi, Analytic Methods of Analysis and Differential Equations: AMADE 2006 (2008), pp. 193–220] and [Dalla Riva, Luzzini, and Musolino, Inverse Problems 38 (2022), 055004] from Schauder to fractional Sobolev spaces. For the EFIE, the single layer representation and the surface Piola transformation give the result in Maxwell trace spaces, whereas the result for open surfaces or screens is obtained by introducing suitable restriction and extension by zero operators. As opposed to existing results, we do not rely on an affine-parametric representation of the boundary deformations, thus allowing for more general parametric shape variations. Finally, we establish shape holomorphy of the shape-to-solution map for the EFIE, subject to interior electric Maxwell nonresonance on closed surfaces but with no such condition on screens. Under suitable summability and stability assumptions, these shape holomorphy results provide an analytic basis for the dimension-robust convergence of interpolation and quadrature methods used in computational uncertainty quantification (UQ) of scattering problems with high-dimensional, shape-parametric uncertain geometry.

Deep learning provides a flexible mesh-free framework for solving elliptic interface problems. However, domain-specific neural approaches often rely on separate networks for individual subdomains, causing the model complexity to grow rapidly as the number of subdomains increases. To address this limitation, we propose a Domain-Specific Adaptation Network (DSAN), which combines a shared backbone with lightweight subdomain-specific adapters to provide local represen- representation flexibility without replicating a complete network for each subdomain. We further establish a stability and error analysis showing that the continuous physics-informed residual controls the solution error, and decompose the resulting error into approximation, optimization, and sampling components. Numerical experiments on two- and three-dimensional problems with multiple regular and irregular interfaces demonstrate that DSAN achieves accuracy comparable to or better than fully decomposed multi-network methods while requiring substantially fewer trainable parameters. More- over, the parameter savings become increasingly pronounced as the number of subdomains grows, demonstrating the scalability of the proposed domain-specific adaptation framework.

Emotion-Cause Pair Extraction (ECPE) requires identifying the causes associated with emotions expressed in a conversation. Accurate extraction can depend on evidence that is not initially available, making it important to decide when further information is worth acquiring. We study agent-guided evidence acquisition for ECPE, where a student agent selectively accesses expert judgments for borderline relations on both sides of its validation-selected F1 decision boundary and revises only queried predictions. Through controlled comparisons under different information-access conditions, we examine how delegation granularity, query selection, and response integration affect prediction quality. At a nominal 10% query rate, selective fusion improves mean pair F1 by 2.64-3.88 points over the student in our main experiments, reaching 65.14 on ECF and 49.74 on MEC4 across model families. Our analysis suggests that greater access does not always translate into better cause identification. These findings motivate acquisition strategies that consider both the relevance of newly available evidence and its effect on prediction revision, providing an empirical basis for more effective and efficient evidence acquisition in ECPE.

Test-time compute (TTC), which scores multiple candidate actions at inference time, is a powerful way to improve the execution performance of vision-language-action (VLA) models, but existing methods keep the policy frozen, so the gain must be recomputed at every execution. We propose Verify, Act, Distill, a framework that consolidates the gains of TTC into the VLA itself. A fixed verifier scores candidates generated by a flow-matching VLA, the weighted aggregate is executed, and the observations and aggregated chunks from successful adaptation episodes are distilled directly into LoRA parameters with the standard flow-matching loss. This reuses supervision that TTC has already produced during execution, without additional reinforcement learning or rollouts dedicated to teacher generation. On the 40 LIBERO tasks with a SmolVLA 5k checkpoint, distilling from only 10 episodes per task raises the mean success rate of verifier-free single-candidate generation from 54.1% to 70.6%, retaining about 74% of the improvement obtained by aggregating eight candidates. Applying the same aggregation to the distilled policy further raises the success rate from 76.4% to 82.3%, with a particularly large gain on LIBERO-Long (44.0% to 57.8%), and the single-candidate policy also improves on LIBERO-plus, which contains distribution shifts. These results show that using verification as a learning signal, rather than only as an execution-time selector, both retains the improvements of TTC and re-amplifies the effect of subsequent TTC.

Implicit time integration is the standard way to overcome the tight CFL time step restriction when solving nonstationary PDEs numerically. However, within an adaptive time accurate integration, the time step size selection is governed not only by stability but also by accuracy requirements. Therefore, an eligible question to ask is: is (unconditionally) stable implicit time stepping really needed if the time step is restricted by accuracy considerations anyway? And how much do we then lose (in terms of the time step size) when switching from the expensive implicit time stepping to stabilized explicit schemes? An answer to this question is also important because such a switch is often done when solving large scale nonstationary PDEs on massively parallel computers. This paper attempts to answer these questions by numerical tests for two particular adaptive time accurate settings: (i)~nonstationary convection-diffusion equations and (ii)~nonlinear heat equations.

We present MARL-BattleGrounds (MARL-BGs), an easy-to-use JAX-native benchmark for heterogeneous and competitive multi-agent reinforcement learning (MARL), designed to be sample-efficient, computationally efficient, and researcher-centric. MARL benchmarks are typically simple and efficient, like SMAX, where winning reduces to unit micromanagement, or rich and costly, like Dota 2. MARL-BGs fills this missing middle. Its first mode, Team Deathmatch, is a simultaneous turn-based game between two teams of five heterogeneous agents. The five classes have distinct basic, passive, and ultimate abilities designed to synergize with allies and counter enemies. Our 52 hand-designed maps with diverse obstacles include a 12-map curriculum and ten held-out validation and test maps. MARL-BGs provides two canonical evaluation modes. First, eight endgame scenarios form a hard generalization challenge: each asks a team to win an unseen, nearly lost position against a strong reactive controller within 5-10 ticks. Second, a monthly round-robin tournament retrains each submission on equal compute, plays it against every member of the current "Big Nine" field, and publishes the Elo results on the official leaderboard. All entrants are publicly released as downloadable opponents. MARL-BGs records 11,192 metrics per game in 28 topics. We also include three strong scripted opponents, an analytical replay viewer, and off-the-shelf tools for self-play, cross-play, curriculum learning, and zero-shot coordination evaluation. We even provide an API for LLM-based agents and use it to evaluate Qwen3.5-9B against our strongest policy. In our BattleClient, humans can play alongside or against any mix of policies, enabling human-AI evaluation. We benchmark MARL-BGs with six additional deep MARL baselines, which we release. On one RTX 5090 with 1,024 parallel games, the simulator runs 50,000 5v5 game steps per second.

This paper develops adaptive movable-antenna (MA) array structures to enhance wireless sensing performance under arbitrary SNR conditions, using the AoA estimation MSE as the sensing metric. Due to the presence of strong sidelobes in the ambiguity function of sparse MA arrays, the classical CRB of AoA estimation MSE fails to characterize the true MSE in the low and medium SNR regimes, rendering CRB-optimized antenna position vector designs suboptimal for MA-enabled sensing. We derive a deterministic MSE approximation that captures the local estimation error within the mainlobe of the ambiguity function and the outlier error induced by sidelobes, providing a tractable and accurate optimization objective. We then propose three adaptive MA structures that are tailored to different hardware and computational requirements. For systems with fully independent motors, a movable free array is optimized by a two-stage greedy algorithm, which approaches the performance of the globally optimal exhaustive search but with lower computational complexity. Halving the required motors, a movable nested array fixes the dense inner subarray and adjusts only the outer-subarray spacing, reducing the optimization to a one-dimensional search. As the most hardware-efficient design, a movable twin array is proposed to adjust the inter-subarray spacing only with a single motor, while still achieving significant MSE reduction over fixed array geometries. Numerical results show that the derived approximation closely matches the true MSE compared with existing performance bounds, and that the proposed structures outperform the CRB-optimized designs by orders of magnitude in MSE across the tested low-to-medium SNR range. Moreover, it reveals that in the low-SNR regime, APV reconfiguration is more effective for improving estimation accuracy than simply increasing the number of fixed antennas.

We discuss the measurement of the Hubble constant ($H_0$) in flat $\Lambda$ cold dark matter cosmology based on the blind hierarchical analysis of 11 multiply-imaged quasars (hereafter the TDCOSMO-2026 sample) and described in greater detail in a companion paper. In addition to the time delays, we use lens models based on high-resolution imaging from the Hubble Space Telescope (HST) and from the James Webb Space Telescope (JWST), analyzed jointly with axisymmetric dynamical models based on JWST-NIRSpec, VLT-MUSE, and Keck-KCWI spectroscopy. Our primary result $H_0=71.1^{+2.4}_{-2.3}$ km.s$^{-1}$.Mpc$^{-1}$ is based on the TDCOSMO-2026 sample, in combination with $\Omega_{\rm m}$ constraints from the DES-Dovekie supernova (SN) dataset. Our 3% precision accounts for the mass-sheet degeneracy. Importantly, our measurement is independent of the local distance ladder (LDL). Among individual late-universe probes, only the traditional LDL is more precise. We discuss our result in the context of the Hubble tension, the difference between $H_0$ measured in the late universe and the prediction based on early-universe probes such as the cosmic microwave background (CMB). We construct combinations of independent late-universe probes and show that the tension with the Planck CMB prediction is robust to excluding any one of the methods based on Type-Ia Supernovae, Cepheids, or the Tip of the Red Giant Branch. For example, we construct a 'no-SN' $H_0$ measurement, by replacing the DES-Dovekie constraint on $\Omega_{\rm m}$ with that from DESI baryon acoustic oscillations, and then combining TDCOSMO-2026 with independent non-SN late-universe probes. This 'no-SN' late-universe probe is in 3.7$\sigma$ tension with Planck. Even after completely excluding the LDL, the tension with Planck persists at the 2.7$\sigma$ level.

We establish dimension-free, pointwise optimal lower-deviation bounds for convex functions under spherically symmetric Cauchy-type measures. These bounds use either mean-variance normalization or moments about the median, the latter covering the Cauchy case where the mean and variance are unavailable. By approximation with a parametrized family the Cauchy-type measures, our results recover the Gaussian setting of Paouris and Valettas \cite{PaourisValettas18} and strengthen their variance-sensitive estimate to a sharp bound, with a complete equality characterization. This goes beyond the partial improvements obtained in subsequent work. We also prove an Ehrhard-type inequality for arbitrary convex sets under these Cauchy-type measures in every dimension and characterize all equality cases. This resolves a conjecture posed by Byczkowski, Małecki and Żak \cite{ByczkowskiMaleckiZak22}. The proof follows from a variational argument combined with the joint concavity of fiber rearrangement. The geometric inequality reduces distributions of convex observables to one-dimensional convex transforms, yielding the sharp lower-deviation bounds.

Existing Chinese social-bias benchmarks for large language models largely rely on normalized or template-based expressions, leaving the influence of internet slang, emoji, and sarcasm insufficiently examined. Safety alignment may further compress conventional plausibility ratings toward the lower end of the scale. This study constructs 73 paired probes across gender, region, and occupation. Each probe contains a neutral expression, a social-media-style expression, and a reversed-identity control. The task is reframed from direct plausibility judgment to social consensus estimation. Social-media expressions are divided into stylistic packaging, which preserves semantic polarity, and sarcastic packaging, which reverses surface polarity. Six Chinese-capable large language models are evaluated through paired differences measuring identity bias, stylistic packaging, and sarcasm shift. All models show significant identity-bias effects; five show significantly negative stylistic-packaging effects; and sarcasm shifts display a clear cross-model gradient. These findings demonstrate that expression form is not a transparent carrier in bias evaluation and that lower scores under sarcasm should not be interpreted directly as bias mitigation. The proposed paired design offers a measurement approach for Chinese social-media contexts while also revealing the construct boundary and prompt sensitivity of social consensus estimation.

Integrated nonlinear photonics demands waveguides that simultaneously offer ultra-low-loss, relatively strong nonlinearity, and tight mode confinement. Tantalum pentoxide (Ta2O5) is attractive for this purpose because it combines a broad transparency window, relatively strong third-order nonlinearity, and favorable thick-film growth characteristics. In tightly confined Ta2O5 waveguides, however, enhanced interaction between the optical mode and etched sidewalls makes scattering loss an important limitation for achieving high Q anomalous-dispersion resonators. Here, we mitigate this confinement-scattering trade-off in pure Ta2O5 waveguides using a fabrication flow based on the Damascene concept. The resulting microring resonators (MRRs) with a cross-section of 1.6 {\mu}m x 0.85 {\mu}m exhibit intrinsic quality factors exceeding 4.0 x 106, corresponding to propagation losses below 10 dB/m, while maintaining anomalous dispersion suitable for bright dissipative Kerr soliton operation. Using these resonators, we generate a coherent bright single-soliton microcomb with a repetition rate of 108.32 GHz. Under optimized dual-pump operating conditions, the platform further exhibits an experimentally accessible single-soliton window spanning 7.5 GHz, indicating a large detuning tolerance for soliton operation; this broad operating window is consistent with the relatively weak thermo-optic response of Ta2O5. Thermal-bistability analysis further indicates that the residual scattering loss is comparable to the material-absorption loss, rather than dominating the loss budget. These results demonstrate that low optical loss, tight mode confinement, and dispersion engineering suitable for soliton formation can be jointly achieved in a pure Ta2O5 platform, providing an ultra-low-loss platform foundation for integrated nonlinear photonic devices and more complex chip-scale nonlinear photonic systems.

Experience-based learning enables large language model (LLM) agents to improve over time by reusing knowledge from past executions. However, existing methods typically rely on final task outcomes as feedback for experience learning, overlooking the execution process and limiting their ability to evaluate and optimize experience based on trajectory quality. To address this limitation, we propose TQG-Exp, a trajectory-quality-guided experience-based learning framework that introduces process feedback. Specifically, we introduce Trajectory Quality Loss (TQL), which jointly considers task completion and process quality to provide a learning signal beyond final task outcomes. Based on this signal, we employ paired rollouts with and without retrieved experience to guide experience optimization. Representative trajectories are selected based on their outcomes and trajectory quality to extract task-level and task-type-level experiences. Meanwhile, differences in trajectory quality between the paired groups are used to estimate the contribution of retrieved experience and update its utility. The learned utility is then combined with semantic relevance to guide subsequent experience retrieval. Experiments on ALFWorld, WebShop, and ScienceWorld with two backbone LLMs show that TQG-Exp outperforms existing experience-based methods, improving Avg.@3 over the strongest baseline by 4.50 and 8.55 percentage points on DeepSeek-V4-Flash and Qwen3.5-Flash, respectively.

Within the framework of multivalued dynamical systems, we compute the Conley index for a class of limit cycles in planar Filippov systems. We classify these cycles according to their interaction with the switching manifold, including crossing, sliding, and mixed regimes. Using the Conley index for multivalued admissible maps developed by Mrozek, we construct the appropriate index pairs and determine the corresponding indices for each class. These computations enlarge the class of Filippov invariant sets for which the Conley index is known and extend previous results on low-codimension singularities to periodic dynamics.

While contrastive learning is widely used to learn deterministic representations, it does not inherently provide estimates of uncertainty. Post-hoc uncertainty estimation methods, such as the Linearized Laplace approximation (LLA), offer a way to quantify uncertainty without retraining the encoder. However, we show that directly using the LLA induced distribution over the contrastive embedding does not yield reliable pointwise uncertainty estimates for downstream tasks: embedding variance alone does not reflect whether decisions such as nearest-neighbor retrieval or cluster assignment are stable. To address this limitation, we develop a post-hoc framework based on LLA that propagates encoder uncertainty through the downstream task. We characterize the curvature of contrastive objectives and introduce positive-semidefinite repairs where needed to obtain valid local Gaussian approximations without retraining the encoder. We test the proposed approach in metagenomic binning and image classification tasks. For metagenomic binning, posterior coassignment probabilities support consensus partitions and the selection of reliable cores, leading to improvements over existing baselines. Additional image classification experiments show calibration improvements on standard benchmarks and real histopathology datasets.

Let $A=\mathbb{Q}[t^{\frac{1}{2^n}}:n\geq 0]$ and consider $A[u,u^{-1};\sigma]$, a skew Laurent polynomial ring, where $\sigma(t^q)=t^{2q}$. We study the kernel of derived extension of scalars along $ A[u,u^{-1};\sigma]\longrightarrow\mathbb{Q}[u,u^{-1}], $ the quotient by $\mathfrak{m}A[u,u^{-1};\sigma]$, with $\mathfrak{m}=(t^{\frac{1}{2^n}}:n\geq 0)$. A finite free resolution of $\mathfrak{m}A[u,u^{-1};\sigma]$ over $ A[u,u^{-1};\sigma]\otimes_{\mathbb{Q}} \bigl(A[u,u^{-1};\sigma]\bigr)^{\mathrm{op}} $ proves smoothness. A specialization inequality for matrix ranks supplies a nonzero exact colimit-preserving functor that vanishes on every compact object, proving failure of compact generation.

Aspect Sentiment Quadruple Prediction (ASQP) is fundamentally a relational reasoning problem: identifying aspect-opinion-category-sentiment quadruples requires modeling structured dependencies, not merely sequential co-occurrence. Existing LLM-based approaches incorporate syntactic information indirectly, via retrieval-based demonstration selection or multi-stage training, rather than as unified, single-pass generation-time context. We present DRIFT, which linearizes dependency parse trees and injects them directly into LLM prompts as explicit relational context, enabling the model to reason over aspect-opinion dependencies rather than infer them from token proximity alone. DRIFT further integrates retrieval-augmented in-context learning and a syntax-aware LLM-based adjudication mechanism that complements exact-match evaluation under span-boundary variation. On SemEval Rest15, Rest16, and ACOS, DRIFT achieves the strongest performance among compared generative ASQP methods, reaching 54.47% and 64.10% F1 on Rest15 and Rest16, with consistent gains across short- and medium-distance aspect-opinion configurations; adjudication further shows exact-match metrics systematically underestimate semantically correct predictions.

The iHowe duality for iquantum groups of type AIII/IV was established in \cite{LX22} via two approaches, based on partial flag varieties and quantum coordinate coalgebras respectively. In this paper, we provide a new construction of this iHowe duality via quantum differential operators. Moreover, by deriving explicit action formulas, we prove that our construction coincides with the two constructions given in \cite{LX22}.

By predicting future states, latent world models provide rich self-supervision for end-to-end driving, but often inherit dense features from pretrained visual encoders as their world-state interface. This creates a mismatch: visual pretraining produces information-rich, spatially dense features, but their adaptation for motion-conditioned world modeling and planning is deferred to downstream training. The dense grid also makes future prediction more computationally expensive as visual resolution increases. We therefore argue that video pretraining should directly learn state representations suited to downstream world modeling and planning, rather than relying on downstream training to adapt inherited visual features. We propose ***MORE***, a V-JEPA framework that learns **M**otion-**O**riented **RE**gisters during video pretraining as a shared state interface for driving world models and planning. MORE injects temporally aligned ego motion into a small set of registers and uses them as the sole context for masked patch prediction, channeling dense patch-level supervision through a compact state bottleneck. A complementary blockwise register-masking objective further shapes predictive structure in the register space. During downstream training, the same register space defines the future states predicted by the world model and provides shared scene memory for trajectory generation and scoring. On NAVSIM-v2, MORE outperforms the state of the art by 1.6 in EPDMS, while achieving superior efficiency with only 1/10 the inference latency of DriveLaW. These results support learning the state interface for world modeling and planning directly during video pretraining.

In this paper, we prove a global $C^{2,\alpha}$ estimate for the complex Monge–Ampère equation with a positive $C^\alpha$ right-hand side on a compact Kähler manifold.

Linear stability analysis predicts the onset of wrinkling, while weakly nonlinear analysis determines whether the bifurcation is supercritical or subcritical through the sign of the cubic amplitude coefficient. When this coefficient vanishes, higher-order terms are needed. In this paper, we develop a higher-order Stroh framework for weakly nonlinear post-bifurcation analysis of finitely deformed elastic solids. For each nonzero harmonic, the same base-state Stroh operator is retained at every order, with nonlinear source terms assembled from lower-order fields to account for geometry, constitutive laws and constraints. This recursive structure, together with Fredholm solvability conditions, enables us to derive cubic, quintic and higher-order amplitude equations. Here, we demonstrate the power of this framework by analysing wrinkling in an incompressible neo-Hookean film bonded to an exponentially graded substrate. The results recover established linear instability benchmarks and the supercritical-subcritical transition in the homogeneous-substrate limit. For graded substrates, the cubic coefficient vanishes on a surface in the parameter space of modulus ratio and substrate gradation. On this surface, the quintic coefficient takes both signs, corresponding to supercritical and subcritical bifurcations. These regions are separated by a curve along which the quintic coefficient also vanishes. Determining the branch direction along this curve requires higher-order terms, which can be calculated within the same framework.

We construct an equivalent norm on $\mathbb{R}\oplus\ell_2$ and a nonempty closed convex unbounded subset having the fixed point property for nonexpansive self-mappings. The ambient renormed space has the fixed point property on bounded closed convex subsets. The main point is a geometric localization estimate at a distinguished point of the unbounded set; the fixed point conclusion then follows from the Kirk–Ray localization theorem.

In this work, long-time Sobolev stability and error estimates with optimal $\varepsilon$-dependence are established for the Strang splitting method applied to the Allen–Cahn equation with periodic boundary conditions. By combining the modified energy dissipation law, and Hölder-Gagliardo-Nirenberg product estimates, the numerical solution is proven to admit uniform-in-time $H^r$-seminorm bounds $\mathcal{O}(\varepsilon^{-r}+1)$, consistent with the corresponding Sobolev bounds of the exact solution. A second-order error estimate $\mathcal{O}(\varepsilon^2\tau^2)$ is further established on any prescribed finite time interval, exhibiting quadratic dependence on $\varepsilon$. Numerical experiments are presented to verify the optimal $\varepsilon$-dependence of both the stability and error estimates.

Cross-modal Thermal Geo-localization (TG) provides an illumination-robust positioning solution for Unmanned Aerial Vehicles (UAVs) in Global Navigation Satellite System (GNSS)-denied environments. However, existing thermal geo-localization methods mainly focus on near-nadir observations or depend on map-side elevation priors, limiting their applicability to continuous oblique thermal localization with only geo-referenced 2D satellite maps. To address this problem, we propose ScalLoc, a scale-aligned local-to-map localization framework for continuous oblique thermal UAV geo-localization. ScalLoc follows a reconstruction–refinement–anchoring–propagation design: it reconstructs local window geometry from thermal sequences, refines camera poses using track-based pose optimization, adaptively anchors each window to the satellite map, and propagates validated states to recover frame-level global trajectories. To support systematic evaluation, we construct Thermal-Oblique, a real thermal UAV sequence dataset containing 216 urban and rural day–night trajectories and 28,112 thermal frames with frame-level annotations. Extensive experiments demonstrate that ScalLoc reduces the mean localization error from 112.69 m to 26.97 m compared with the VGGT-only configuration, corresponding to a 76.07% reduction, and achieves the lowest frame-weighted mean position error among the compared methods. These results demonstrate the feasibility of continuous oblique thermal geo-localization using only lightweight 2D satellite maps, without requiring digital surface models or preconstructed 3D maps. Code and dataset are available at https://github.com/FloralHercules/ScalLoc.

Imminent blast furnace relinings create a consequential investment window for U.S. primary steel decarbonization. Using plant-level capacity planning and stochastic operations modeling, we quantify the costs, infrastructure, and fiscal requirements to transition legacy blast furnace sites to direct reduction under supply-side incentives. Under baseline assumptions, post-subsidy premiums above average blast furnace costs, including relining, are 272 to 427 dollars per ton of steel for near-zero-emission hydrogen-based direct reduction and 115 to 181 dollars for natural-gas-based production. Representative facilities producing two million tons of steel annually at legacy locations require approximately 4 to 6.5 and 0.7 to 1.1 GW of renewable generation and battery storage, respectively. This translates to 65 and 12 GW across the unrelined fleet for hydrogen- and natural gas-based pathways, respectively. These findings connect replacement timing to costs, infrastructure, and public support, motivating a sequenced transition through clean-powered natural-gas-based direct reduction to avert blast furnace relining, reduce emissions by 57 percent relative to blast furnaces, and preserve options for deeper decarbonization through hydrogen substitution or carbon capture.