Papers

Multimodal language models often need to reason about the physical dynamics of the world in order to answer questions appropriately. Various methods have emerged for solving physical reasoning tasks, and in particular, two leading approaches are Chain-of-Thought reasoning and physics-grounded simulation. However, relatively little is known about which particular problems can be solved by each approach. Some tasks may benefit from computationally expensive generative video simulations, whereas others may be solved equally well (or even better) with language-based reasoning. Our work addresses this by systematically comparing simulation and language reasoning across a variety of multimodal tasks involving physical reasoning, such as answering questions about fluid dynamics and elasticity. We draw a parallel with this to resource-rational theories of human cognition, which propose that people optimally trade off simulation and reasoning depending on task demands. We present a novel cognitively-inspired hybrid model which optimally trades off simulation and reasoning to improve model performance and computational efficiency. Our model is able to decide the appropriate method to solve a physical reasoning problem at test time, and finds an optimal balance between accuracy and cost. Further, our model can be trained on a smaller vision-language model that is only 4B parameters and deployed to improve performance on much bigger base models with $>$3T parameters like Gemini 3 Pro.

Grand Unified models of particle physics inevitably give rise to magnetic monopoles. Often the model will also contain a weakly broken discrete symmetry that leads to the formation of biased domain walls that survive for a limited period in cosmology. For a range of the discrete symmetry breaking parameter, domain walls can collapse to form magnetically charged extremal black holes lighter than $\simeq 1\, {\rm kg}$ but these are not expected to survive until the present epoch due to Hawking evaporation and Schwinger pair production of monopoles. If the parameter is smaller still, the black holes may be astrophysical, with mass greater than $10^{15}\, {\rm g}$ and with sub-extremal magnetic charge: $Q \simeq 10^8$ (for our canonical choice of parameters). The cosmological energy density in residual magnetic monopoles depends on the discrete symmetry breaking parameter and for sufficiently small values of the parameter, the magnetic monopole density can satisfy all observational constraints.

While LLM-based agent systems have demonstrated remarkable proficiency in reasoning and solving complex real-world tasks, they also come with substantial token consumption and inference latency, limiting their practical deployment. To enhance the efficiency of agent systems, recent efforts have focused on transferring agentic capabilities from large-scale models to small language models (SLMs) via supervised fine-tuning-based distillation. Nevertheless, as interaction trajectories grow longer, involving extended reasoning-action chains and extensive environmental feedback, distilled student agents tend to experience progress stagnation: becoming trapped in unproductive loops characterized by persistent failed strategies and difficulty making meaningful progress. Our systematic analysis shows that this phenomenon consistently occurs across diverse SLMs and task domains. To address this issue, we propose Progress-Aware Distillation (ProD), which explicitly detects and penalizes stagnation in student-generated trajectories. ProD encodes the stagnation gap between student and teacher into an adaptive margin for dynamically penalizing possible stagnation. By iteratively applying this procedure, ProD enables student agents to progressively approximate teacher behavior. Extensive experiments involving 8 SLMs, ranging from 0.6B to 8B parameters, on both in-domain and out-of-domain benchmarks, demonstrate that ProD substantially mitigates progress stagnation while enhancing both the success rates and task-completion efficiency of distilled SLM agents.

Vision-language-action (VLA) policies fine-tuned on LIBERO are trained and evaluated on the same ten instruction strings, and rewording the instruction changes base OpenVLA's success by -38.0 points. Test-time prompt ensembling, which improves language models, does not recover this loss in any setting we ran. Paraphrase consensus (the medoid action over K paraphrases) costs base OpenVLA 16.8 points when the training instruction is a member. Without it, the medoid of the paraphrases scores -32.4 points relative to the training instruction, and confidence-based selection scores -28.0. The same medoid over samples of one paraphrase improves on greedy decoding but stays -27.6 points below the training instruction, consistent with aggregation reducing variance without removing the bias the paraphrases share. A wrong-instruction probe measures how much of a policy's success depends on the instruction. Across three policies and four suites, paraphrases cost a policy only where this share is high, and the stronger policies lose a much smaller fraction of it than base OpenVLA. LoRA post-training on paraphrased instructions reduces the one-paraphrase effect to +2.0 points, against -32.0 for a matched control, reproduces across two seeds and on OpenVLA-OFT, transfers to withheld phrasings, and leaves the policy's reliance on the instruction unchanged.

We shall study birational maps of moduli spaces of stable sheaves on a K3 surface with Picard number 1 induced by Fourier-Mukai transforms.

Unsupervised feature selection (UFS) is of great significance in image processing and pattern recognition. Nevertheless, existing model-based methods often rely on manually tuned hyperparameters, while deep learning-based methods generally require massive training data. To address these issues, this paper proposes an efficient manifold deep unfolding feature selection network (MDUFS-Net). Technically, we first incorporate the $\ell_{2,0}$-norm into the classic principal component analysis (PCA) framework, then unfold the alternating direction method of multipliers (ADMM)-based iterative algorithm into an end-to-end trainable network, thereby enabling automatic parameter learning. Moreover, a manifold optimization strategy is developed to improve the numerical robustness. On this basis, we further extend MDUFS-Net into an enhanced variant called MDUFS-Net+ by introducing the $\ell_{0}$-norm for more discriminative feature representations. Extensive experiments validate that our proposed MDUFS-Net and MDUFS-Net+ outperform state-of-the-art methods in the UFS task, with promising performance in clustering. Our code is available at https://github.com/xianchaoxiu/MDUFS.

We develop and analyze a three-dimensional pure source transfer domain decomposition method (PSTDDM) for the Helmholtz equation in free space. Extending the two-dimensional PSTDDM proposed by [Du and Wu, J. Sci. Comput., 83(2020),83:68], the proposed method transfers sources successively along the $x_1$, $x_2$, and $x_3$ directions, yielding layer-wise, bar-wise, and block-wise PSTDDMs. The main challenge in the convergence analysis is deriving wavenumber-explicit truncation-error estimates. To address this challenge, we establish inf–sup conditions for the uniaxial perfectly matched layer (UPML) problem under relaxed restrictions on the PML parameters and reformulate the source-transfer operators. We then introduce a positive-definite reconstruction step that produces a globally conforming approximation. In addition, a new quantitative lower bound is established for the imaginary part of the complex PML distance, more easily yielding exponential decay estimates in three dimensions. These lead to wavenumber-explicit convergence estimates for all three PSTDDMs. Numerical experiments demonstrate the effectiveness of the proposed methods both as direct solvers and as preconditioners for GMRES.

Let $p$ be an odd prime, and let $\rho\colon G\to \GSp_{2n}(\Z_p)$ be an irreducible symplectic residually multiplicity free representation. We define the symplectic extension graph $\Gamma_\rho^\GSp$ associated with $\rho$ to be the directed graph whose vertices are the residual factors of $\rho$ and a directed edge between two vertices corresponds to a nonsplit extension between the vertices realized by $\rho$. Using the Euclidean Bruhat–Tits building associated with $\GSp_{2n}(\Q_p)$, under some assumptions, we prove the existence of certain paths in $\Gamma_\rho^\GSp$ and show that $\Gamma_\rho^\GSp$ is a disjoint union of nonempty strongly connected subgraphs. Moreover, we provide examples to show that the result we obtain is optimal.

Static benchmarks for large language model (LLM) agents face saturation and data contamination risks, motivating continual updates to evaluation tasks. However, aggregate scores and success rates offer limited insight into specific problem-solving bottlenecks and provide limited guidance for subsequent task design. We propose EvoProbe, an evaluation-driven benchmark evolution framework that integrates task generation, diagnostic evaluation, and feedback-driven regeneration into a closed loop. It combines verifiable subtask outcome scoring with evidence-supported multi-judge trajectory evaluation and distills phase-level bottlenecks, success patterns, and failure patterns into diagnostic feedback for generating new executable tasks. Across two rounds of cybersecurity experiments, evaluations of eight models on 66 tasks reveal phase-level performance differences and common failure patterns beyond aggregate scores. In a cross-round comparison with the Examiner model set and solver configuration held fixed, all eight models achieve lower Outcome scores on the updated tasks, with relative decreases of 11.8% in mean Outcome and 40.0% in mean Pass\textasciicircum{}3. These results support using fine-grained diagnostics to guide iterative task updates and probe agents' current capabilities and limitations.

Comparing financial disclosures across languages requires identifying shared accounting concepts and recovering all numerical facts that express them. Existing benchmarks evaluate aspects of these capabilities, but provide limited insight into whether both succeed on the same multilingual evidence. In particular, it remains unclear whether language models can recognize these concepts across languages and exhaustively recover their corresponding numerical evidence from the same contexts. We introduce MULTIFINGROUND, a benchmark designed to investigate this recognition-grounding gap in multilingual financial reports. Constructed from FY2025 disclosures of 90 issuers in English, French, and Greek, MULTIFINGROUND aligns independently authored reports through a shared accounting taxonomy and provides traceable fact-level annotations. The benchmark evaluates financial fact identification, concept recognition, exhaustive fact selection, and concept discrimination without candidate labels. Across 15 evaluated models, eight API and open-weight reference models achieve 97.3-99.4% concept recognition accuracy, yet miss at least one target fact in 26.6-41.9% of correctly recognized groups. Further analyses reveal substantial variation in concept discrimination and limited gains from the evaluated finance-specialized models. Our findings demonstrate that strong concept recognition can coexist with incomplete evidence recovery, highlighting the importance of evaluating semantic recognition and evidence completeness together.

This paper presents $S^3$-Nav, a structured spatial-semantic decision-making framework for language-guided robot navigation under partial observability. Rather than assuming a complete environment representation in advance, $S^3$-Nav incrementally constructs persistent spatial-semantic state while exposing only a capacity-controlled, task-conditioned view to the high-level policy. This separation decouples what the robot must retain from what the policy needs to inspect, allowing decision complexity to be controlled without discarding grounded evidence required for subsequent reasoning and validation. High-level navigation outputs remain provisional and are independently grounded and validated against persistent semantic evidence and current geometric observations before physical execution or task termination. Evaluations across multiple environments and object- and relation-goal tasks demonstrate that separating persistent state, decision-facing evidence, and execution authority improves closed-loop navigation reliability while reducing policy reasoning cost.

We propose a potential projection (PP) method for the nonlinear Schrödinger equation (NLSE) with low-regularity and singular potentials by replacing the potential with its Fourier projection (truncated Fourier series). This gives rise to an NLSE with projected potential (NLSEwPP). We rigorously establish its well-posedness under low-regularity potentials, and its convergence to the original NLSE. The NLSEwPP is then directly discretized by the standard time-splitting Fourier pseudospectral (TS-FP) method with the mesh size chosen according to the potential projection parameter, resulting in the fully discrete TS-PP-FP method. Numerically, TS-PP-FP consistently achieves optimal temporal and spatial convergence rates with respect to the regularity of the exact solution under low-regularity and even singular potentials. Compared with the time-splitting Fourier spectral method, TS-PP-FP attains the same convergence rates at significantly lower computational cost and preserves the mass conservation and time symmetry (that are lost in the Fourier spectral discretization of the time-splitting method); compared with the time-splitting FP method, it is substantially more accurate for low-regularity potentials with the same computational cost.

This paper presents a comprehensive comparison of four representative reinforcement learning (RL) methods in autonomous vehicle (AV) decision-making, including: Fitted Value Iteration (FVI), Rollout Classification Policy Iteration (RCPI), Deep Q-Network (DQN), and a discrete-action adaptation of Deep Deterministic Policy Gradient (D-DDPG). The four methods are applied to the same AV decision-making problem at an unsignalized intersection and are compared in terms of optimality and safety, training stability, and training and decision cost. RCPI is the closest to a reference solution and has the most stable training process. However, it is the least data-efficient. D-DDPG reaches the second-smallest gap to a reference solution with the highest data efficiency, but has the least training stability. DQN is the most stable model-free method but has the highest collision rate. FVI achieves a lower collision rate than DQN, but is less data-efficient and less stable. Based on these results, we provide suggestions for selecting a method according to whether a model is available, the budget for training, and whether stable training is required.

Multivariate Hawkes models are widely used to measure endogenous interactions in event data, but latent common signals can generate apparent excitation even without structural interaction. We characterize the resulting linear projection and construct stable, nonnegative Hawkes processes that share the mean intensity and Bartlett spectrum of common-signal models despite having different excitation mechanisms. This establishes a concrete form of second-order non-identification. We derive integrated third-order cumulants for Hawkes processes with Cox immigration and establish generic local identification of normalized structural parameters in two- and three-dimensional systems. An exact-equivalence Monte Carlo experiment demonstrates how third-order information can distinguish mechanisms with identical second-order structure, while revealing substantial finite-sample limitations under weak signals. For a restricted parametric family, we develop Whittle estimation from binned counts, establish consistency and asymptotic normality under appropriate identification conditions, and construct feasible sandwich standard errors accounting for estimated mean intensities. Simulations assess structural recovery and inference accuracy. An application to cryptocurrency transactions illustrates the sensitivity of inferred excitation to model specification and the limitations of structural interpretation based on spectral fit alone.

Legal reasoning is a fundamental capability for large language models (LLMs) to complete legal AI tasks such as legal judgment prediction. In legal practice, this reasoning is shaped by legal philosophy: a judge's view of the nature and sources of law guides how legal materials are interpreted and applied, so judges working from the same statutes and precedents can reach different judgments. Existing research has largely overlooked whether LLMs can understand legal philosophy and apply it in legal reasoning, an ability we call legal-philosophical reasoning. To fill this gap, we introduce LePhilBench, a benchmark for evaluating the legal-philosophical reasoning of LLMs that comprises two benchmarking tasks and a dataset. The two tasks evaluate how well LLMs understand legal philosophy and how well they apply it in legal reasoning, respectively. The dataset is manually and meticulously constructed. Its test set contains 220 U.S. Supreme Court opinions. A law professor designed fourteen annotation questions on legal philosophy, and three law-trained annotators with formal training in jurisprudence answered all fourteen questions for every opinion, yielding 9,240 legal-philosophical labels. LePhilBench takes the first step toward exploring legal-philosophical reasoning in LLMs.

We study Dirac points for a two-dimensional scalar Helmholtz equation in a periodic dielectric medium with two penetrable inclusions per honeycomb cell. In a joint small-inclusion and high-contrast regime, we reduce the Bloch eigenvalue problem to a two-dimensional interaction matrix and derive a two-term asymptotic expansion for the two relevant eigenvalues, uniformly for quasi-momenta separated from the reciprocal lattice. At a vertex K of the Brillouin zone, rotation and inversion-conjugation symmetries force these eigenvalues to coincide. A Schur-complement analysis of the exact operator pencil, together with a nonvanishing lattice Green-function coefficient, proves that the resulting double eigenvalue has a nonzero conical splitting and gives an asymptotic formula for the conical slope in the scaled eigenvalue. For fixed sufficiently large contrast, symmetry-preserving changes of variables and analytic perturbation theory then continue this Dirac point as the inclusion size varies: it remains nondegenerate except at a relatively closed discrete set of admissible sizes.

Agentic capabilities are increasingly important for modern LLMs, yet remain difficult to evaluate during pretraining. Existing approaches typically rely on static trajectory-derived tasks or likelihood-based proxies, which are lightweight but provide limited visibility into how base models behave in interactive environments. We introduce ASAP (Agent Scaffold Adaptation for Pretraining Evaluation), a lightweight framework for eliciting and evaluating agentic behavior from pretrained base models on end-to-end tasks. Rather than converting base models into chat-style agents, ASAP preserves the completion interface and adapts existing agent scaffolds through structured trajectory continuation, short reference prefixes, and minimal recovery mechanisms. Across software-engineering and deep-research benchmarks, ASAP yields discriminative end-to-end performance across base models and pretraining checkpoints. Beyond aggregate scores, ASAP exposes model-generated execution trajectories, enabling analysis of exploration, editing, testing, recovery, and task completion across training stages. These trajectories provide a behavioral view of how agent-relevant capabilities change during pretraining and how execution patterns differ after post-training. Our results suggest that end-to-end agent evaluation can complement conventional pretraining benchmarks by providing a practical diagnostic of interactive model behavior.

LLM system capabilities depend not only on model parameters but also on the executable harnesses that organize information acquisition, tool use, reasoning, and memory. Recursive harness evolution can automate their design, but how it can reliably discover generalizable systems from limited, noisy, and repeatedly reused feedback remains unclear. We study this question in agentic video understanding, where rich multimodal evidence and coupled mechanisms make harness optimization challenging. We first introduce VideoHarness-BRSI, a recursive self-improvement framework that evolves video harnesses around a frozen vision-language model. Analyzing over 4,000 evolved candidates, we find it competitive with hand-engineered systems but identify three interconnected failure modes: validation overfitting, search-budget dilution, and the early-experience trap. We trace all three to a common root: the same imperfect validation evidence drives both harness revisions and the proposer's search strategy. We therefore propose VideoHarness-SRSI, an evidence-governed framework in which every search decision rests on evidence that is transferable, sufficient, and gathered before the search commits. It restricts the proposer to content-free feedback, informs exploration with instrumented warm-up experiments, and develops mechanisms in isolated probe-race branches before factorial composition and joint refinement. Across four video understanding benchmarks, VideoHarness-SRSI improves the equally weighted mean held-out score by 6.2% relative to VideoHarness-BRSI and reduces the mean validation-test gap by 37.9%. Reliable harness evolution thus depends on how search is organized and informed, not only on how well it optimizes validation performance.

Configuring distributed LLM training across hundreds of GPUs requires jointly optimizing tensor, pipeline, expert, context, and data parallelism alongside micro-batch size, recomputation, sharding, and overlap, a combinatorial space where memory legality can hinge on a single byte of activation accounting. Today, teams navigate it through expensive multi-node trial and error, burning GPU-hours on crashes and suboptimal recipes. We present Primus Projection, which closes this loop with two coupled components. First, a hybrid projection engine that measures what it can and simulates what it cannot: GPU microbenchmarks on as few as a single device capture compute kernels and any in-scope communication; a sub-node downscale-measure-upscale workflow analytically restores out-of-scope collectives, FSDP overlap, and the full pipeline schedule at the multi-node target. A pure simulation mode runs entirely on CPU, enabling pre-silicon planning without any GPU. Second, the Primus Tuning Agent treats the projection engine as a fast scoring oracle (seconds per candidate instead of tens of minutes) and uses it to drive an intelligent search over the configuration space. A deterministic seed planner sweeps single axes; an LLM investigation loop proposes cross-axis combinations the planner cannot reach, with an analytic memory pre-filter that rejects infeasible candidates before any GPU time is spent. Validated on Llama 3.1 (dense) and Mixtral 8x22B (MoE) across two GPU generations, all projections stay within ~10% of measured multi-node throughput, and fidelity holds at production scale: 4.7% error on DeepSeek V3 671B at 1,024 GPUs and 1.9% on Qwen3-235B-A22B at 256 GPUs. In a Mixtral 8x22B case study, the Primus Tuning Agent discovers a configuration delivering +27% throughput over the published 4-node BF16 reference at the same scale, in under 30 minutes of single-node exploration.

Large language model (LLM) agents accomplish complex tasks through multi-turn interactions with external tools. However, malicious content embedded in user queries, tool descriptions, or environment observations can manipulate their decisions and induce unsafe actions. Adversarial co-evolution has emerged as an effective approach to strengthening LLM safety, but existing work primarily focuses on language-level safety or indirect prompt injection in web tasks. In this paper, we introduce AgentSafeEvo, a co-evolutionary reinforcement learning framework for agent safety built on an attacker-defender game spanning diverse tasks and attack types. The attacker learns to construct adversarial agent tasks that expose weaknesses in the defender's tool use, while the defender learns to complete tasks safely under these attacks. We further introduce learnability-guided task weighting, which uses within-task defender-reward variability to adjust each task's contribution to attacker and defender updates. Extensive experiments on agent safety and general capability benchmarks demonstrate that our method improves adversarial robustness while maintaining general agent capabilities.

Softplus affine\((1,1)\) models keep the conditional mean positive while allowing coefficients of either sign. We study them under Poisson, negative binomial, gamma and related conditional distributions. A stationary solution with moments of all positive orders exists whenever the coefficient sum is less than one, strictly enlarging previously known sufficient regions. At the unit root, the coefficient sum equals one. Under an invertibility condition, a stationary solution exists in this case if and only if the intercept is negative. At a stationary unit root, the conditional mean has a power-law tail with an explicit index, and the observations can exhibit long memory. For a fixed softplus scale, the Poisson quasi-maximum likelihood estimator is consistent and asymptotically normal at the usual \(\sqrt n\) rate below and at the unit root, with the coefficient sum left unrestricted in estimation. At the unit root, these results require only a finite mean and yield standard Wald inference even when the observations have infinite variance or long memory. Simulations and two applications examine finite-sample inference and sensitivity to the softplus scale.

Simulated environments enable scalable training data generation for embodied agents, but more data does not necessarily provide what a particular agent needs to learn. Existing environment-generation pipelines largely optimize generic properties such as realism, diversity, or task coverage, while different pretrained policies can fail for different environmental reasons. We therefore introduce WEDGE, a framework for weakness-guided navigation learning in which the failure modes of a pretrained agent guide the generation of training environments at each adaptation round. Given a pretrained policy, WEDGE uses an LLM to propose executable weakness features from contrasting successful and failed rollouts, automatically validates them on the diagnostic set, and selects the strongest validated weakness based on its success-rate gap. The validated weaknesses are then mapped to the environmental factors that control them. WEDGE varies these factors to construct environments in the difficulty regimes where the policy struggles, producing targeted training experience for adaptation. Across three navigation agents with different adaptation mechanisms, we find that policies exhibit distinct weakness profiles and benefit from different training environments. Weakness-conditioned adaptation consistently outperforms matched random and hard-example alternatives on ProcTHOR, while the resulting gains for Uni-NaVid and Gemini also extend to HM3D after ProcTHOR adaptation. Iterative re-diagnosis further shows that dominant weaknesses can persist or shift as the policy improves, providing updated guidance for subsequent environment construction. Together, these results show that policy failures are not only diagnostic signals, but actionable guidance for constructing training environments that target a policy's current weaknesses.

MLLM-based detectors formulate vision-language grounding as autoregressive coordinate generation, yet in dense scenes, they often collapse into a box repetition loop, repeatedly emitting identical boxes until the decoding budget is exhausted. We trace this failure to historical-answer attention takeover: Under full-history autoregression, repeated coordinate tokens in the growing answer history attract disproportionate attention, crowding out the attention sinks needed to attend to new visual evidence. % To break this loop, in this paper, we propose Compressed Window Auto-Regression (WinAR). This new mechanism partitions a long answer sequence into consecutive generation windows and restricts full token-level autoregression to the current window only while compressing each previous window into a fixed set of latent tokens that condition subsequent decoding. This design reduces the repeated exposure to raw historical coordinates that triggers the attention takeover, yet preserves cross-window dependencies essential for coherent multi-object generation. On RSDense, which contains 200-2,000 objects per image, our model WinARDet improves RexOmni F1-score (IoU=0.5) from 32.16 to 39.36 over the baseline, while reducing the redundancy rate from 35.48% to 13.00%. WinARDet also generalizes across decoding strategies and output formats, including parallel box decoding and polygon generation, providing a practical paradigm for long-horizon vision-language grounding across scene densities.

Lyapunov exponents characterize the average rate at which nearby trajectories in phase space converge or diverge and therefore provide a useful criterion for dynamical stability. In this work, we develop a general framework for analyzing Lyapunov exponents in stationary spacetimes and extend previous studies beyond circular orbits. For a generic stationary spacetime described by $g_{\mu\nu}(r,\theta)$, we show that the phase space relevant to linear perturbations is spanned by $(r,p_r,\theta,p_\theta)$ and the corresponding linear stability matrix has rank four. When the spacetime admits a rank-2 Killing tensor, the linear stability matrix can be reduced to a block-diagonal form, allowing the Lyapunov exponents to be obtained analytically. By imposing the appropriate constraint conditions, the formalism further yields the linear stability matrices and Lyapunov exponents for circular and spherical orbits. The validity of the method is illustrated by several representative examples, including the (inverted) harmonic oscillator, planar Kepler motion, and particle motion in Schwarzschild and Kerr spacetimes. These results provide a unified framework for investigating the stability properties of particle orbits in both classical and relativistic dynamical systems.

We provide a distributed online algorithm for multi-agent submodular coordination in bandit environments, i.e., environments whose evolution is unknown a priori and may even adapt to the agents' actions. We are motivated by multi-robot tasks such as target tracking, where the optimal actions change over time and the agents must track them rather than a single fixed optimum. To address such problems, we provide the Optimistic Distributed Online Greedy (O-DOG) algorithm, that leverages predictions about the environment's behavior and improves regret guarantees. The agents select actions simultaneously over arbitrary, possibly time-varying, network topologies, and each agent acts optimistically, i.e., leveraging predictions of its upcoming rewards, e.g., from forecasts of the targets' motion and of its neighbors' actions. We bound O-DOG's tracking regret in terms of the agents' prediction error and the bound never exceeds its prediction-free counterpart. Particularly, it is sublinear even when the optimal action changes at every time step, provided the predictions are accurate enough. We further quantify the suboptimality due to decentralization as a function of the network structure, and show that accurate predictions accelerate convergence. We validate O-DOG in simulated multi-robot target tracking.

We show that limit-periodic Jacobi matrices in the weak exponential class $EC(\eta)$ have purely absolutely continuous spectral type when $\eta$ is sufficiently large, depending only on the $R$-boundedness constant. The proof first establishes homogeneity of the spectrum from the weak exponential approximation rate. A closure theorem for reflectionless Jacobi matrices then transfers reflectionlessness from the periodic approximants to the limit, and a theorem of Poltoratski and Remling rules out singular spectrum on a homogeneous set.

We revisit the extraction of parton distribution functions (PDFs) in the pion in a global QCD analysis of pion–nucleus Drell–Yan and leading-neutron (LN) electroproduction data, in view of recent suggestions that uncertainties on the pion PDFs at small parton momentum fraction $x$ are dramatically underestimated. We perform a set of controlled fits that vary the LN data coverage, PDF parametrization, and positivity constraints, determining both the PDFs and pion-nucleon splitting functions simultaneously. While the use of a restricted H1 LN data sample used by the Fantômas group is found to enlarge the PDF uncertainties and admit solutions with vanishing gluon PDFs, our global analysis provides a good description of an extended H1 and ZEUS LN database, significantly reducing the parametrization dependence and strongly disfavoring a zero gluon distribution.

We introduce FormCraft, a framework for representing acquired operations as first-class capabilities that can be recursively composed, directly invoked, and selectively retained in a persistent library through domain-specific verification. The framework separates capability well-formedness and public callability from later admission to persistent storage while preserving formation provenance and operational identity. We formalize recursive compositional closure over a uniform capability space and show that formed composites can be reused through the same public interface without re-forming their historical derivation. Experiments across continuous, discrete, propositional, and sequence domains demonstrate instance-independent reuse, independent checking, persistent acquisition, and reduced reuse-time search work under first-class exposure.

Virtual reality training for robot-assisted vascular intervention requires accurate robotic control and effective feedback on guidewire–vessel interactions. This paper presents a VR training system combining asynchronous dual-mode command mapping with sensorless interaction estimation. The system supports velocity-controlled navigation and position-driven incremental manipulation. Guidewire deformation and a Hunt–Crossley-type contact response are combined and temporally filtered to estimate interaction intensity, while trajectory-based visualization supports post-procedure review. Tests confirmed distinct command-dispatch patterns across three velocity gears and the position mode. During hybrid-scene navigation, the estimated response remained low during straight insertion and increased as the guidewire bent within the vascular model. Trajectory analysis yielded a model-derived cumulative trauma work (CTW) value of 15.166 in normalized units and localized regions of elevated interaction. In a preliminary study with 15 novices, physical-phantom task success increased from 53.3% to 93.3% after VR training, while mean completion time decreased from 132.4 s to 96.7 s. These results demonstrate the system's dual-mode operation, deformation-sensitive feedback, and potential to improve subsequent physical-phantom task performance.

The optical Kerr effect in high-refractive-index membrane metasurfaces patterned with a square lattice of five-pointed star-shaped pores is investigated numerically using gallium phosphide as a model material. The star geometry supports resonances with pronounced electromagnetic energy confinement, including an anapole state. The sharp tips of the star-shaped pores concentrate the electric energy density in air, exceeding that of Mie voids by a factor of seven. The effective second-order refractive index is enhanced by up to three orders of magnitude relative to bulk GaP, with the largest values obtained near the anapole resonances. The nonlinear response remains stable under polarization rotation and random misalignment of the nanoholes, indicating tolerance to fabrication imperfections. These results establish star-shaped pore lattices in freestanding membranes as a promising platform for nonlinear optics exploiting strong field confinement.