Papers

Let $L$ be a smooth Hermitian holomorphic line bundle on a compact complex manifold $X$ of dimension $n$, and let $r$ be its maximal curvature rank. For every fixed holomorphic vector bundle $E$, we prove $h^q(X,L^p\otimes E)=O_\varepsilon(p^{r+\varepsilon})$ for every $\varepsilon>0$ and every Dolbeault degree, with the sharp bounds $h^0,h^n=O(p^r)$ at the endpoints. The curvature may have variable rank and arbitrary signature, and no global foliation or Kähler assumption is imposed. The all-degree estimate follows from local rescaling and holomorphic restriction estimates that remain uniform across rank changes. An independent maximum-principle argument locates the maximal rank of a section map at a semipositive curvature point; it yields $\kappa(L|_{X_0})\le r$ on each connected component $X_0$ and gives the endpoint bounds.

Rapid progress in AI agents has brought growing attention to agent safety, with extensive evaluation focused on digital environments. As agents move into the physical world, embodied safety becomes increasingly important: failures can cause human injury and costly hardware damage. Beyond selecting safe actions, embodied agents must also operate under real-time constraints: the physical world does not pause while an agent reasons. As pedestrians move and vehicles approach during inference, an action that appears safe at observation time may become unsafe before execution. Real-time embodied safety therefore depends on both decision quality and decision latency. We introduce RT-SAFE, a simulated urban benchmark for evaluating embodied-agent safety under real-time constraints. RT-SAFE combines navigation tasks with moving actors, environmental hazards, and traffic rules, while allowing the world to evolve throughout inference and action execution. Across eight VLMs, agents achieve high task completion yet almost never complete safely: in the hardest setting, only 0.7% of episodes finish without a safety event. More strikingly, matched static and real-time evaluations yield task completion rates of 91.3% and 94.1%, respectively, while real-time execution increases collisions by $12.3\times$. These results reveal that standard task success can mask substantial safety failures, and that decision latency itself can become a source of physical risk. Finally, we show that RT-SAFE can support offline RL training and substantially reduce collision rates while achieving strong task completion.

Can an agent's predictions reveal whether its reasoning is based on a classical or a quantum model? Using known results on matrix factorizations, here we show that quantum Bayesian retrodiction can produce one-step-ahead forecasts incompatible with every classical Bayesian explanation based on learning about a fixed but unknown sampling law from conditionally independent observations. The separation has a sharp threshold in the number of outcomes: for any measurement with at most four outcomes, the quantum predictions admit a classical realization, irrespective of the prior state and the finite Hilbert-space dimension, whereas a five-outcome measurement on a single qubit already violates an explicit classical bound. This bound holds for arbitrary classical latent states, prior probabilities, and sampling laws, and involves only the agent's initial and updated predictions. Thus, in this setting, quantum Bayesian retrodiction is strictly more expressive than classical Bayesian learning, and this difference can be witnessed without observing or specifying the agent's internal description.

While dependent quantization in H.266/VVC delivers a high compression ratio, its strong serial nature and high complexity result in poor real-time performance, making it difficult to deploy in practical scenarios. To improve the real-time performance of dependent quantization with minimal degradation to its compression performance, we propose a interleaved parallel dependent quantization hardware architecture with low BDBR loss, which achieves four-channel parallel dependent quantization by time-division multiplexing most combinational logic. This architecture adopts the proposed intra-CG context simplification scheme and the encoding scheme that skips decAbslevel during rate estimation. The proposed design incurs a BDBR loss of only 0.42% under the All Intra configuration and 0.38% under the Random Access configuration, respectively. Implemented in Verilog HDL, the dependent quantization hardware architecture achieves quantization speeds of 4K@33.2, 91.4, 331.2, and 454.1 fps at QP = 22, 27, 32, and 37, respectively, when implemented on the Xilinx XCZU19 FPGA. When implemented on ASIC using the TSMC 28nm process standard cell library, the corresponding quantization speeds reach 4K@84.0, 231.0, 837.0, and 1147.7 fps.

Achieving human-level dexterity in complex, unstructured environments requires the seamless integration of whole-body scene interaction and dexterous object manipulation skills. While existing physics-based controllers generate physically plausible behaviors in each domain, they largely address these two capabilities independently. In this paper, we present Co${}^{2}$Skill that integrates scene interaction and dexterous manipulation through a unified policy formulation. Built on a pretrained motion prior, the policy uses task and phase dependent observation masks to select information relevant to the current interaction goals. We introduce a goal-conditioned loco-manipulation curriculum that combines partial reference guidance for precision with exploration from varied initial states while allowing goal-directed execution beyond the demonstrated trajectories. We further introduce a cross-task curriculum that jointly trains individual skills and selected task sequences, preserving physical states across task boundaries and maintaining grasps during subsequent scene interactions. Together, these support sequential task execution and simultaneous scene interaction with object manipulation. We evaluate sitting, standing, climbing, stair traversal, and goal-directed manipulation, together with sequential execution and with random different conditions. Additionally, we demonstrate skill compositions in indoor environments, illustrating their integration within the same control formulation.

The Aharonov-Regev proof that $\mathrm{GapCVP}_{c\sqrt n}$ lies in $\mathsf{NP}\cap \mathsf{coNP}$ uses a verifier that tests dual lattice vectors; its proof gives $c=100$. We study this verifier through a linear program in which a certificate is modeled as a sample from a probability distribution on the dual lattice. This viewpoint gives an exact analysis of the close-target tests: adding gradient and Hessian checks increases the certified close radius from $\sigma^{-1}/4$ to $\sigma^{-1}\sqrt{3/16}$, and higher derivatives cannot improve it within this framework. With Gaussian certificates for far targets, we obtain $$\mathrm{GapCVP}_{c\sqrt n},\ \mathrm{GapSVP}_{c\sqrt n}\in \mathsf{NP} \cap\mathsf{coNP}$$ for every $c>2/(\pi\sqrt3)\approx0.3676$. An appendix gives a finite-bit implementation of the verifier. We also show that the Gaussian certificate is not always optimal and solve the unbounded-support program exactly for targets of order two, where its value is determined by the spectral capacity of an odd dual coset.

Fluvial corridors mediate dynamic river-groundwater exchanges and support major transportation infrastructure, yet continuous subsurface monitoring remains limited by sparse point sensors and infrequent time-lapse surveys. Addressing this observational gap is critical during extreme flood events, when transient saturation, pore-pressure buildup, and structural scour drive complex hydro-mechanical changes that threaten both riparian slope stability and bridge foundations. Here, we demonstrate that traffic-excited highway bridges act as persistent, spatially fixed seismic sources; their vibrations, recorded on roadside telecommunication fiber with Distributed Acoustic Sensing (DAS), enable time-lapse imaging of river corridors. We evaluate this approach using dark fiber recordings along South Korea's Gyeongbu Expressway during a record monsoon flood in July 2025, targeting a 430 m multi-span bridge crossing the Miho River. Vehicle impacts excite flexural resonances of the bridge deck, generating a discrete spectral comb of fundamental-mode Rayleigh waves in the surrounding ground; these 3-6 Hz waves propagate beyond 400 m across both riverbanks to image the alluvial section down to bedrock. Because bridge-structure geometry constrains the source location and dominant modal frequencies, virtual source gathers achieve rapid convergence within 5 min of ballistic wave stacking with high waveform repeatability over the recording period. Relative seismic velocity (dv/v) monitoring resolves velocity drops up to 1.0% during flood passage associated with heavy precipitation and river stage rise, consistent with hydrological softening of the riparian sediments. These results demonstrate that traffic-excited bridges provide persistent, repeatable seismic illumination, turning roadside telecommunication cables into dense arrays for both hydrogeophysical and civil infrastructure applications.

Many rare genetic diseases are associated with recognizable craniofacial features. However, traditional approaches for describing facial morphology rely largely on qualitative clinical observation and free-text descriptions, which are often subjective, non-standardized, and difficult to reproduce across observers and institutions. Although the Human Phenotype Ontology (HPO) provides controlled terms for describing facial features, these terms are typically categorical rather than quantitative and may vary depending on examiner experience and interpretation. Here, we present FaceKit, a computational framework for quantitative facial phenotyping from frontal facial photographs. FaceKit extracts standardized measurements of facial landmarks and derived 120 morphological features, then reports feature-level z-scores representing deviation from population reference distributions. The reference distributions are built from the FairFace dataset spanning diverse ancestral groups. We evaluated FaceKit on a curated subset of the GestaltMatcher Database covering 50 rare-disease cohorts. In addition to quantitative facial analysis, FaceKit includes synthetic facial image generation to support rare disease model development and data augmentation. We also performed privacy evaluation to assess whether synthetic images reveal identifiable information from real patient photographs and could compromise patient privacy. Across disease case studies, FaceKit-derived quantitative measurements captured known facial features associated with rare genetic disorders and provided objective support for clinical phenotyping. Together, these results establish FaceKit as a useful tool for quantitative phenotyping, and has the potential to improve rare disease diagnosis, support genotype-phenotype studies, and enable more reproducible clinical characterization across diverse patient populations.

Naturalistic visual decoding from EEG has long been constrained by cohort size: existing scaling literature caps out at a few dozen subjects, leading prior work to conclude that scaling subject cohorts yields minimal performance gains. Training a cross-modal EEG–video contrastive encoder on a cohort larger by more than an order of magnitude, we find the axis is productive but has an onset. Below $S\approx50$ — the entirety of the range prior work occupies — no model improves meaningfully over an untrained encoder; above it, decoding rises log-linearly in subject count with no saturation at the top of our ladder, on a fitted stimulus-feature probe and on fit-free movie-moment retrieval alike, and the gain transfers to a second, unseen film. How far the axis carries then depends on initialisation more than on capacity: an encoder initialised from an EEG foundation model scales ${\sim}1.6\times$ faster per doubling of the cohort than randomly initialised encoders at two depths, is the only one still converting subjects into retrieval accuracy at the top of the ladder, and converges on a fraction of the alignment compute. Subject scaling on shared naturalistic stimuli is thus an effective and currently unsaturated frontier for scaling EEG foundation models.

LLM agents can generate database operations and explain their results, but current interfaces often leave a gap between generated plans, execution conditions, and claims presented to users. We argue that agent-facing data systems need two enforceable contracts. A plan contract defines what an agent may execute and reference; an evidence contract records the belief state, completeness, and provenance under which a result supports a claim. We instantiate these contracts in TGMS, a bi-temporal graph system in which an LLM plans over a fixed temporal operator interface. A static verifier checks plans before execution, and a claim verifier checks typed claims against content-addressed traces. Live model runs exposed two failures missed by input-only schemas and value-only grounding: nonexistent result fields and page-local counts reported as complete-result counts. Result-field checking makes the first a repairable rejection. Completeness propagation detects the second in all 15 controlled cases and misses all 15 when disabled. On the frozen CollegeMsg workload, TGMS reaches 0.408 typed-answer accuracy versus 0.064–0.284 for the evaluated baselines. On Bitcoin-OTC, direct SQL over the same bi-temporal store matches TGMS, showing no universal accuracy advantage for the fixed operator interface. On correction probes, TGMS and bi-temporal SQL answer historical-belief questions, while latest-state baselines cannot. Before claim gating, 21 of 220 answers contain an unsupported gated claim; after gating, none of 199 emitted answers does, at the cost of 21 fewer answers. The plan contract makes invalid plans rejectable and execution reproducible under recorded conditions, while the evidence contract makes gated claims faithful to cited evidence. Neither guarantees correct interpretation of user intent.

Many applications of physical AI run within finite or closed physical worlds with a limited set of physical laws governing object behavior. Examples include robots working in a warehouse and agents moving around in a video game. In order to better organize, filter, and curate data for physical AI applications, we propose a new approach centered on the unique settings and physical laws of individual datasets. We train LeCuration, a small world model intended to serve as a data curation tool for a separate, larger downstream model. To build this model, we choose LeWorldModel (LeWM)as our latent encoder and predictor, adding a diffusion transformer (DiT) decoder to add visuals to autoregressive gameplay rollout. We find that the embeddings of this model can be used as an anomaly detection signal and as a content-based clustering heuristic, and that auto-regressively predicting the game state with this model allows us to qualitatively check for action-state consistency. This paper presents a qualitative, proof-of-concept case study on CS:GO gameplay data; we do not yet report quantitative curation metrics or downstream training results, which we identify as the key next step.

Wake words face an inherent trade-off: higher sensitivity reduces missed commands but increases accidental activations. In co-located augmented reality (AR), the system must also determine whether the user is speaking to the assistant or to a nearby person. We introduce a new perspective on this problem: combining gaze-based address with an embodied assistant, visible listening status, and turn management across activation, continued interaction, and release. In our implementation, users look at an assistant anchored in the scene and see activation progress and listening status on its body. Sustained gaze opens a local interaction channel; speech and playback keep it open when attention returns to the task; and inactivity closes it. We evaluated this design with 25 participants. After selecting the assistant's placement and dwell duration, each participant worked with a partner to plan a trip while using the assistant. The study recorded 500 interaction outcomes, including 496 assistant-directed utterance attempts. Gaze acquisition completed before speech for 490 of these attempts (98.8%): 467 began while the channel remained open, whereas 23 began after it had been released. The other 6 attempts began before acquisition completed. Among 102 reviewed attempts in which gaze left after acquisition but before speech, the configured retention policy kept the channel open for 79 and released it before 23. The results show that an embodied target with visible status can support clear entry into an assistant interaction while revealing a different problem at release: after users look back to their work, they may not see that the assistant has stopped listening. We contribute the implemented gaze-invocation design and design implications for communicating assistant state after visual attention moves elsewhere.

Robot co-design couples morphology search with policy learning, yet training every new design from scratch discards acquired control experience. We present LACE-CRAFT, which compares continued learning on the current robot with policy adaptation to new morphology-reward pairs. LACE resumes the incumbent's full learning state and initializes compatible challengers with its actor parameters and observation statistics. A fixed task metric selects among both branches and the frozen incumbent. CRAFT coordinates Feedback, Morphology, Reward, and Integration roles through shared experimental records and behavioral replays to generate and cross-review paired proposals. A generative extension converts generated meshes into editable articulated models with configured joints, actuator interfaces, and consistently updated simulation assets. Across five locomotion benchmarks, mean scores over three evaluation seeds are 6.4-91.9% higher than D2C. Both methods train 30 new morphology-reward pairs over five rounds; LACE additionally uses four continuation training units. Five-task ablations examine policy inheritance and replay-derived feedback. A fabricated prototype demonstrates indoor walking and illustrates the geometry-to-hardware workflow.

Common-image gathers (CIGs) contain physically meaningful information about velocity-model errors through reflector focusing and residual moveout, but in conventional imaging workflows they are typically used only as diagnostic tools. In this work, we propose a multiscale self-attention summary network that maps high-dimensional 3D CIG volumes into compact conditioning embeddings for probabilistic subsurface velocity inversion. These learned embeddings preserve offset-dependent kinematic structure and spatial coherence while reducing variability caused by background-velocity mismatch. Conditioned on these summary embeddings, a flow-matching model learns a transport from a Gaussian source distribution to the posterior distribution of plausible velocity fields. Numerical experiments show that, compared with direct conditioning on raw CIGs, the proposed summary network improves posterior velocity inference. In particular, the multiscale attention design provides greater robustness to background-model mismatch, yielding more accurate posterior reconstructions and lower predictive uncertainty.

In Bayesian inverse problems, posterior sampling requires generating samples that are consistent with given observations while capturing the range of plausible solutions. Direct conditional generative models introduce latent noise to model this ambiguity, but paired inverse-problem training can still encourage an almost deterministic map from the observation to the target. As a result, generated samples may be observation-consistent while under-representing posterior variability, especially when the posterior is multimodal, leading to undercoverage, mode distortion, or artificial transitions between distinct feasible solutions. We propose joint twist-flow, an augmented flow-matching formulation that learns a continuous transport from the augmented source state $(z_x, y)$ to the augmented terminal state $(x, z_y)$. Here x is the target variable, $y$ is the observation, $z_x$ is the Gaussian reference coordinate for posterior sampling, and $z_y$ is a Gaussian likelihood-side coordinate associated with the observation branch. Under a Gaussian observation model, $z_y$ is motivated by the normalized observation residual associated with observation compatibility. Its role is not to replace uncertainty in $x$, but to couple generated samples of x to observation consistency, helping reduce likelihood-inconsistent variation while preserving variability in weakly constrained directions. We validate the method on low-dimensional inverse problems with reference posterior samples, where joint twist-flow better preserves multimodal posterior support than a direct conditional-flow baseline. We further evaluate the method on image restoration and seismic subsurface velocity-model inversion, showing increased posterior variability while maintaining observation consistency.

This work examines the transfer of a co-evolved communication mechanism between two robotic agents from a discrete two-dimensional (2D) simulator to a three-dimensional simulator with real physics (3D). The study focuses on whether a communication mechanism co-evolved in a 2D environment retains its functional role after transfer to a 3D physics-based simulator. To support this analysis, the effects of the episode time budget, the social cue, and the asymmetry between the two co-evolved roles were examined. The results indicate that the success rate increased approximately linearly with the evaluated time budgets, with no evidence of a plateau between 2,000 and 6,000 physics steps, suggesting that evaluations based on shorter episodes may underestimate the performance of the trained controllers. In both simulators, the social cue functioned primarily as a jam- assistance mechanism rather than as a navigation guide, although with a more pronounced effect in 2D. Analysis of eight independent evolutionary runs revealed a consistent direction of asymmetry, although its magnitude varied across runs. Controlling the processing order between agents allowed us to rule out an artifact of the physics engine. Finally, the results are discussed in terms of the factors that may contribute to the remaining performance gap observed after transfer.

Online research platforms underpin much of what science claims about people, on the assumption that a human produced each response. Generative AI threatens that assumption by letting participants delegate responses to a chatbot, yet how often they do so remains unclear because prior estimates rely on self-report or automated detection rather than direct observation. We surveyed 2,500 workers on a high quality online research platform and directly observed AI assistance by linking donated ChatGPT histories to platform submission records of weekly ChatGPT users, covering 712,930 submissions across more than 127,000 studies. Although one in eight surveyed workers reported ever using AI on a study and 68% of observed workers had done so, assistance appeared in only 1% of submissions, with no detectable increase over more than 3 years. Assistance was often temporally localized within tasks and highly concentrated among workers, with 5% accounting for 64% of assisted submissions. Where assistance occurred, workers were virtually always paid, even when study instructions prohibited AI use, with overall approval rates similar to those for unassisted submissions. Half of assisted submissions involved bounded responses, outside the scope of the platform's LLM detector for open-ended responses. Taken together, our results do not support the view that AI assistance currently poses an existential threat to online research, but reveal limited payment consequences for prohibited use and gaps in platform safeguards, leaving platforms poorly prepared should that threat materialize.

We study a linear backward stochastic partial differential equation with unbounded observation-adapted random coefficients, motivated by the duality approach to nonlinear filtering. The coefficients depend predictably on the observation history through a control with almost surely finite time-integrated squared norm. The drift, diffusion, and coefficient multiplying the martingale integrand may grow linearly in space. The diffusion matrix may grow quadratically in space and is allowed to be degenerate. Under bounded positive-order spatial derivatives and bounded smooth observation-measurable terminal data, we prove existence and uniqueness in a polynomially weighted Sobolev class up to control-energy stopping times. The proof combines conditional parameter estimates, entropy bounds for likelihoods, stability under the reference probability, and stochastic-flow reconstruction.

Let $K=K(n,m,\Gamma)$ be a Bedford-McMullen carpet with $n>m\geq2$ and $1<\#\Gamma<nm$, and let $\mu$ be a self-affine measure on $K$ with strictly positive weights. We prove that every similitude $f(z)=rOz+a$ satisfying $\mu(K\cap f(K))>0$ has a diagonal or anti-diagonal orthogonal part $O$, without any arithmetic restrictions on the defining bases. Under the same intersection hypothesis, we also show that $r\in n^{\mathbb{Q}}\cup m^{\mathbb{Q}}$ whenever $K$ is not a segment. For isometries satisfying this hypothesis, we further prove that $f(K)$ is simply a translate of $K$, thereby establishing a strengthened form of the 2010 conjecture of Elekes, Keleti and Máthé in this planar self-affine context.

Modern DBMSs expose hundreds of configuration knobs, resulting in a high-dimensional and heterogeneous search space that makes automated tuning costly. Existing ML-based tuning systems typically treat the configuration domain as box-constrained and rely on workload feedback to implicitly capture inter-knob relationships. However, DBMS documentation specifies deterministic knob dependency constraints, particularly ordering constraints, that characterize structurally valid regions of the configuration space. We present CATune, a constraint-aware Bayesian optimization (BO) framework that models deterministic inter-knob ordering constraints as structural components of the search domain. Instead of learning feasibility boundaries through sampled violations, CATune performs optimization within a constraint-consistent subspace. We develop a topology-aware sampling strategy that respects dependency structure during exploration and avoids the inefficiencies of post-hoc constraint handling. To enable automated constraint discovery, we further design a precision-first extraction pipeline that combines LLM-based parsing with reliability safeguards to mitigate hallucinated dependencies. Experiments on PostgreSQL and MySQL using TPC-C and TPC-H workloads show that CATune substantially improves both sample efficiency and final tuning quality across surrogate models and BO frameworks. Under default ranges, CATune reaches the baseline optimum up to 12.5x faster and improves throughput by up to 63.37%. The improvements persist under knowledge-guided reduced ranges and alternative optimization implementations. These results demonstrate that explicitly modeling system-defined deterministic ordering constraints enhances optimization robustness and system stability.

Although spiking neural networks (SNNs) provide an energy-efficient alternative to artificial neural networks (ANNs), their application to remote sensing image dehazing remains limited. A key challenge arises from the coupling between haze-induced high-frequency attenuation and discrete spike thresholding. This interaction suppresses weak responses and fundamentally limits the recovery of edges, textures, and fine details in spiking dehazing models. To address this challenge, we propose the Efficiently Modulated Spiking Neural Network (EM-SNN), a dedicated spiking framework tailored to remote sensing image dehazing. EM-SNN integrates a statistics-driven Threshold-Modulated Leaky Integrate-and-Fire (TM-LIF) neuron to adaptively compensate for haze-induced contrast compression, together with a Spike Sobel Modulation (SSM) module that enhances structural cues and reduces depth-wise attenuation during spiking feature propagation. By jointly modulating activation scales and structural representations, EM-SNN improves dehazing performance while preserving the inherent event-driven sparsity of SNNs. Experiments on HRSD, RICE, RRSHID, and SateHaze1K demonstrate that EM-SNN achieves competitive dehazing performance while consuming only one quarter of the energy of the strong ANN baseline SFRDP-Net.

The Visual Geometry Grounded Transformer (VGGT) marks a significant leap forward in 3D scene reconstruction, as it is the first model that directly infers all key 3D attributes (camera poses, depths, and dense geometry) jointly in one pass. However, this joint inference mechanism requires global attention layers with extremely long sequences that causes a significant latency bottleneck. In this paper, we propose blockwise clustered attention (BC attention) to accelerate the global attention layers in VGGT. By limiting the clustering within HW-friendly neighborhood blocks, BC attention reduces the computation overhead of query clustering as well as the costly data movement between on- and off-chip memory. This enables BC attention to scale to long sequences and deliver practical latency improvements on GPUs. Moreover, we introduce a hashing hyperplane calibration method and a threshold-based error compensation method to reduce clustering errors efficiently, which is a bottleneck in the current clustered attention mechanism. Overall, our experiments on GPU demonstrate that calibrated BC attention accelerates the global attention layers by 2.10-2.63$\times$ and the whole backbone by 1.77-2.35$\times$ with negligible loss (1%) for large scenes. With a small performance loss (< 5%), calibrated BC attention further achieves a 2.26-2.87$\times$ latency improvement on the global attention layers and a 1.90-2.55$\times$ improvement on the backbone.

This paper presents an N:1 resonant switched-capacitor (ReSC) ladder converter of an output voltage that can be regulated continuously below the native N:1 resonant ratio while maintaining high efficiency. The topology can be generalized to any N-to-1 dc-dc conversion application while requiring only a single inductor. Efficient wide-range voltage regulation is realized by operating the bottom stack of the ReSC switches as diodes to maintain their switching always in phase with the inductor current, and hence, circumvent circulating currents that increase the inductor RMS current and ohmic losses under frequency control. A theoretical model has been developed to predict the output voltage and efficiency of the converter, with simulation results confirming its accuracy for N = 1, 2, and 4. A hardware prototype on a printed circuit board is developed to validate the performance of the proposed frequency-controlled regulation scheme. The prototype achieves a peak efficiency of 97% (94.3%) with a load of 30Ohms (resp. 6Ohms) and an efficiency >90% while generating a 9V USB-compatible voltage from a 40V-to-60V input. The measurement results match the model predictions within 0.63% accuracy.

Attention routing requires a signal that predicts the value of attention on the current prefix. We evaluate whether hidden-state extrapolation error, curvature and error change improve this prediction beyond uncertainty, one-step displacement, position and state projections. Paired executions of the final attention layer supply signed next-token loss differences in frozen SmolLM3-3B-Base and Qwen3.5-4B-Base checkpoints. Utility-supervised routers are tested on 100 held-out PG-19 books at an identical causal 20 percent invocation quota. None of six prespecified comparisons shows a positive gain after familywise correction. In Qwen3.5, a parameter-matched fixed-projection control lowers NLL by 0.00356 nats/token relative to the trajectory router (95 percent interval 0.00218 to 0.00487). Secondary results depend on the operation removed, feature location and scoring horizon; frozen thresholds also drift substantially at longer horizons. Actual selected-query execution yields small long-sequence latency reductions with increased NLL, while learned routers remain slower during cached continuation. The study identifies limits on the incremental value of these trajectory summaries and separates allocation quality from measured inference benefit.

We study positive solutions of $Iu+\mu u=k(x)u^p$ in a bounded domain, where $p>1$, the nonnegative coefficient $k$ may vanish on a sanctuary region, and $I$ is a fully nonlinear nonlocal operator uniformly elliptic in the Caffarelli–Silvestre sense. We characterize the sharp existence interval in terms of positive principal half-eigenvalues and prove uniqueness. At the lower endpoint, the solutions vanish uniformly and their normalized profiles converge to the principal eigenfunction. If $k$ vanishes on a sanctuary $\Omega_0$, then, as $\mu\uparrow\lambda(\Omega_0)$, the solutions blow up locally uniformly in $\Omega$. Writing $\phi_0=\phi(\cdot,\Omega_0)$ for the normalized positive principal eigenfunction in $\Omega_0$, we prove \[ \frac{u_\mu}{\|u_\mu\|_{L^\infty(\Omega)}}\to\phi_0, \qquad \frac{u_\mu}{\|u_\mu\|_{L^\infty(\Omega)}^{1/p}} \to\left(\frac{I\phi_0}{k}\right)^{1/p}, \] uniformly in $\mathbb{R}^n$ and locally uniformly in $\Omega\setminus\overline{\Omega_0}$, respectively. Thus the upper-endpoint blow-up occurs on two distinct scales.

Let $k$ be an algebraically closed field of characteristic $0$ or $p\neq3$. We construct a terminal projective 4-fold $X$ and an ample Cartier divisor $D$ such that \[ 3K_X\sim0,\qquad D-K_X\ \text{is ample},\qquad H^0(X,D)=0. \] In char 0, this disproves Ambro–Kawamata effective non-vanishing conjecture. From this example we construct a smooth projective 4-fold $Y$ with a semiample and big Cartier divisor $D_Y$ such that $D_Y-K_Y$ is basepoint-free and big, and $H^0(Y,D_Y)=0$. We also construct a Gorenstein terminal 6-fold with $K\sim0$, other geometric avatars, and a terminal order-5 Jacobian quotient.

We study the fundamental groups of a normal projective Calabi-Yau variety $X$ with klt singularities and of its regular locus $X_{reg}$. We prove that both groups are almost abelian, and that their ranks are determined by the irregularities of finite etale and quasi-etale covers, respectively. Our approach is differential geometric, and relies on recent advances in the geometric theory of complex Monge-Ampere equations.

We present full molecular dynamics simulations that explicitly incorporate the simultaneous interactions between a trapped ion and a bath of neutral atoms. In contrast to conventional molecular dynamics treatments, this framework enables a systematic assessment of how the atomic-gas density influences both the ion's cooling dynamics and its steady-state mean kinetic energy. Our results show that the gas density measurably modifies the ion's average kinetic energy, albeit only weakly, in qualitative disagreement with predictions obtained from standard molecular dynamics simulations. In addition, the calculations indicate that short-range features of the atom-ion interaction potential become increasingly consequential as the atomic density increases. Simulations including many atoms yield higher mean kinetic energies than standard molecular dynamics, a trend we attribute to the transient formation of molecular-ion complexes. Finally, we observe that for a fixed ion, lighter atomic baths lead to a smaller final ion average kinetic energy than heavier atomic baths.

Dependency upgrades can break downstream projects without changing the library interface. Such behavioral breaking changes are difficult for developers to fix, because the failing test does not always point to the root API, the upstream API that causes the break. Existing LLM-based repair methods obtain evidence for the repair from compiler feedback or library documentation. However, a behavioral break produces no compiler feedback and is often undocumented. Agents that receive no upgrade evidence also usually do not retrieve upstream evidence themselves, and most of their failed repairs do not identify the root API. The library diff provides useful upstream evidence, but the root API must first be identified to select the relevant part of the diff. We present BBCFixer, a repair method that runs the failing test under the old and new library versions, ranks the calls whose return value differs to identify a candidate root API, and filters the library diff with that candidate. To evaluate repairs of behavioral breaks, we further introduce BBCBench, a benchmark of 100 behavioral dependency breaks in Python and JavaScript. We compare BBCFixer on BBCBench with two baselines: (1) Pure Agent, an agent that receives no upgrade evidence, and (2) BDUpdater, a method that mines library documentation. BBCFixer raises the average pass rate by up to 17% relative to Pure Agent and needs up to 27% fewer agent steps per successful repair. BBCFixer thus provides a way to select the upstream evidence behind a behavioral break, so that an LLM agent can repair behavioral breaking changes more effectively and efficiently.

Growing wireless traffic is increasing pressure on the congested radio-frequency spectrum. Optical wireless communication (OWC) provides a complementary solution by using the abundant unlicensed optical spectrum. However, indoor OWC networks are dynamic: users move, enter or leave the network, and subscribe to different services. Poorly coordinated resource allocation can consequently waste subcarriers, require excessive transmission power and cause frequent AP reassignments. Energy efficiency (EE), defined as the total delivered data rate divided by the total network power consumption, therefore requires the serving AP, number of allocated subcarriers, and transmission power to be jointly adapted while maintaining QoS. Optimising these in a dynamic time series, multi-service OWC environment produces a complex sequential EE optimisation problem. To address this problem, this work proposes Dual-Agent Resource Allocation using Deep Reinforcement Learning (DARA-DRL). DARA-DRL combines a branching duelling deep Q-network for association and subcarrier allocation with a conditional soft actor-critic agent for continuous power control. The agents are coupled through a common reward and a cooperative value update that evaluates each discrete allocation together with its corresponding power decision. Simulation results show that DARA-DRL remains within 5% of the optimal solution and, compared with state-of-the-art benchmarks, it improves EE by 28.8% and QoS satisfaction by 10.5%, while reducing online decision time by 14.5%. Results demonstrate that agent specialisation simplifies mixed-action learning, and cooperation outperforms independently trained agents.