Papers

Hyper-redundant robots are well suited for confined-space manipulation due to their high dexterity, but safe operation in cluttered environments remains challenging. In addition, their slender structures often lead to uneven load distributions and nonuniform tracking errors along the body. To address these issues, this work proposes a weighted control barrier functions (W-CBFs) framework that enforces safety constraints while reducing tracking errors caused by uneven loading. The proposed controller was first evaluated on a circular path-following task under different obstacle configurations. With fixed weights, compared to the non-weighted method, the maximum reduction in root-mean-square (RMS) tracking error was 59.6% in simulation and 87.7% in physical experiments. An adaptive weighting strategy was then investigated based on the discrepancy between simulated and experimental performance under different mapping functions. The RMS errors were further reduced by 21.9% and 8.5%, respectively, although the error increases when obstacles were located close to the robot body. Finally, the robot was evaluated in a cleaning task requiring coverage of a rectangular area and compared with manual teleoperation. Although the controller was not explicitly optimized for area coverage, the autonomous strategy achieved comparable or better coverage performance while avoiding collisions with the surrounding frame, whereas collisions occurred during manual operation.

In this paper, we propose MECT, a speaker verification model that integrates the Mixture-of-Experts (MoE) mechanism into a CNN-Transformer backbone with optimized block structure and stacking scheme. Specifically, we investigated four MoE variants that span utterance-level and frame-level granularity with dense and sparse routing strategies. The MoE mechanism proves to be effective over the baseline without MoE with only a small increase in parameters. We further scale MECT to a series of model sizes, all maintaining compact parameters and low computational complexity. In particular, MECT-B2 achieves state-of-the-art performance on VoxCeleb1 and delivers strong results on CN-Celeb, demonstrating its effectiveness across diverse datasets. In addition, we establish a streaming inference paradigm through causal retraining, which maintains strong performance at a chunk size of 100ms.

Groups of HI-rich galaxies are key laboratories for understanding galaxy evolution and environmental effects, constructing samples of such groups is fundamental for relevant studies. Using the FAST All Sky HI Survey (FASHI) Data Release 2 (DR2), currently the largest and deepest HI catalog available, we identify galaxy groups directly from HI signals, without relying on optical pre-selection. A group-finding algorithm with a density contrast criterion and a minimum membership of five yields a catalog of 459 galaxy groups containing 3015 HI sources. Using archival spectroscopic data, we identify optical counterparts and derive total stellar masses of member galaxies as a proxy for the group total mass. The group redshift distribution peaks at z ~ 0.02, and the total HI mass peaks at ~ 10^{10} M_{\odot}. We find a significant positive correlation between total HI mass and total stellar mass, consistent with the increase in HI mass with halo mass reported in previous stacking studies. The ratio of total HI mass to total stellar mass decreases significantly with increasing total stellar mass, indicating gradual HI depletion in groups. Our sample provides rich targets for future studies of galaxy evolution and large-scale structure in the local Universe.

Semantically meaningful subtask labels can provide useful contexts for long-horizon policies, but automatically identifying both reliable temporal boundaries and broad semantic descriptions for annotations remains difficult. We present an automatic labelling pipeline that assigns temporal localisation to deterministic trajectory analysis and semantic interpretation to vision-language (VL) reasoning. The pipeline segments synchronised kinematic signals into phases, performs phase-localised VL reasoning to describe the contents, and aggregates the outputs for the base, left arm, and right arm actions. We evaluate this pipeline primarily on 29 real Galaxea bimanual mobile-manipulation tasks. Repeating the VL reasoning three times first produces the same output value for 87.4% on selected tasks. A review by nine participants across all 29 tasks then judgements on the labelled phases and shows positive acceptance of temporal divisions (90.5%), body labels (90.7%), and arm labels (78.7%). The results indicate that the segmentation-VL design can produce structured annotations while preserving asynchronous bimanual behaviour, providing a basis for richer semantic subtask identification and state-based verification.

Multilingual scene text recognition (STR) remains challenging due to the scarcity of training data for most languages and the difficulty of serving diverse scripts within a single model. Existing solutions either deploy one recognizer per language, inflating cost and introducing error accumulation, or rely on massive vision-language models (VLMs) that are expensive and still inaccurate on many scripts. In this work, we pursue an all-in-one multilingual recognizer that is simpler than per-language experts, lighter than VLMs, and more accurate than both. First, we construct TextMuSS-10M, a large-scale synthetic scene text dataset spanning 10 scripts and 229 languages. It provides balanced and sufficient supervision where real data is unavailable. Second, we propose ScriptMoE, a script-aware Mixture-of-Experts (MoE) architecture. It shares a single visual encoder and replaces the dense decoder with a sparse MoE block, which consists of an image-level router dispatches each image to the top-2 script-aligned experts and a shared expert absorbs cross-script knowledge. Extensive experiments on our assembled TextMuSS-Bench (10 scripts, 10,899 images) show that ScriptMoE achieves the highest accuracy of 82.06%, outperforming the strongest STR baseline by 1.31%. On the CC-OCR end-to-end multilingual task, replacing only the recognizer in PP-OCRv5 with ScriptMoE lifts F1 score from 65.71% to 80.89%, slightly surpassing the best VLM (80.73%) at a fraction of the parameter count.

Medical image interpretation is central to diagnosis and care, yet adapting general-purpose multimodal large language models (MLLMs) often requires resource-intensive domain-specific fine-tuning. Here we introduce representation-guided in-context learning (RG-ICL), a training-free inference framework that retrieves query-aligned demonstrations using frozen encoders, without task-specific parameter updates. Across eight datasets spanning histopathology, radiology and retinal fundoscopy, RG-ICL improved classification (mean gain 20 percentage points) and visual question answering (VQA) (mean gain 13 percentage points) over no-context and conventional ICL, approaching or exceeding training-based comparators. Which cases were retrieved mattered more than how many: 6 query-aligned cases outperformed up to 32 randomly selected ones, whereas fixed or random cases often reduced accuracy below baseline. For VQA, aligning reference cases with both image content and question intent produced further gains. These findings indicate that for medical image interpretation, curating which reference cases an MLLM sees is a practical alternative to retraining it.

We show the height at time $t$ of the standard continuous-time ballistic deposition process has variance at most $C_d t, t \geq 1$ in every dimension $d \geq 1$. The crucial idea is to adapt a martingale argument due to Aldous, which gives tail bounds on first hitting times for monotone surface growth processes. Inverting these tail bounds and applying a duality theorem due to Penrose yields a linear variance bound for the height of ballistic deposition.

Robots can recover from failures by asking bystanders for help, but effective human-in-the-loop recovery requires communication that accounts for differences in people's knowledge. Prior inverse-semantics work generates requests using a single listener model, leaving differences in listener knowledge untested. We introduce Listener Differences in Human-Robot Interaction (LD-HRI), a game, dataset, and benchmark that evaluates speakers through human listener performance. Our evaluation examines request properties, large language model (LLM) speakers, and inverse-semantics request-selection algorithms under controlled differences in listener information. The corpus contains 446 human-written requests and 1{,}302 listener trials. We additionally evaluated 24 frozen LLM-written requests with 70 human listeners across 560 trials. Novice success is descriptively higher with model-written requests across all four tasks, yet both request sources leave substantial expert–novice gaps, including 16 percentage points for LLM requests. LD-HRI makes these gaps measurable, providing a foundation for designing more robust communication in human-robot and human-agent interaction.

Intermittent visual loss disrupts target-relative feedback during underwater orbiting, making it difficult to maintain coordinated motion and reacquire a moving target. We present AquaOrbit, a reinforcement-learning controller with a recovery module for underwater target orbiting under interrupted visual feedback. During detection loss, the recovery module uses latched line-of-sight, roll, and depth references to support stabilization and target reacquisition. We train the controller in Isaac Sim with dynamics, observation, and vision-loss randomization. Evaluated without retraining in Gazebo/ROS2 under a different physics engine and perception perturbations, AquaOrbit completes 20/20 orbiting trials in each of the static- and moving-target conditions on an unseen variable-depth 3-D trajectory. In the moving-target condition, it reduces mean line-of-sight error by approximately 46% relative to a PID-based visual servoing controller with recovery while maintaining comparable path-tracking accuracy; removing the recovery module reduces completion to 9/20. Zero-shot physical deployment with fully onboard perception and control demonstrates elliptical, figure-eight, and variable-depth circular trajectories, including the latter two trajectory types absent from training. The robot maintains attitude stability during manual occlusions lasting up to 8s and reacquires the target within 2.5s in the reported attitude-induced field-of-view loss events.

Comparisons of confounding-control methods are informative only when simulated data contain the treatment-covariate relationship those methods address. We assessed whether Plasmode 0.1.0 preserves that relationship, uses the returned exposure to generate outcomes, and reports the effect implied by its generating model. We inspected the source and ran the generator under identical seeds with source rows as supplied, sorted by observed exposure, or using an alignment correction. We ran 200 null-effect replicates per strategy in a synthetic cohort and the SUPPORT/Right Heart Catheterisation cohort. A sampled subject usually received another subject's exposure probability. In the synthetic cohort, source-model AUC was 0.503 before and 0.841 after alignment. Crude risk-difference bias moved from +0.0051 to +0.3037. Other orders preserved or reversed the association. After alignment, deliberately misspecified estimators retained risk-difference biases of 0.10-0.11. Correctly specified estimators were nearly unbiased. With the unmodified generator, all five appeared similarly unbiased. At an injected odds ratio of 2, the conditional log odds ratio appeared on the observed exposure (+0.696; target 0.693), not the returned exposure (+0.017). Misalignment can weaken, preserve, or reverse designed confounding and thereby distort method comparisons. Alignment correction does not repair outcome-exposure decoupling, disagreement between the reported and generating effects, or marginal miscalibration.

Crash datasets that carry an investigator narrative hold information the coded fields omit. Coding those narratives at scale has been blocked by three obstacles. Frontier large language models are costly at that scale, their generated text cannot be verified, and no rule says how much output a human must check. This paper formulates narrative coding as gated, typed decisions answered by Jev, a System One model that returns probabilities over analyst-defined options and generates no text. A screen covered 499,500 Texas narratives and 195,857 were coded with a 27-question schema. Cost is governed by schema size rather than narrative length. The probabilities are audited against coded fields and against 2,416 blinded human judgments drawn under a stated sampling design. Two frontier large language models are benchmarked on the same records. Against human labels the typed model attains an F1 of 0.908. One frontier model gains 0.059 and the other is indistinguishable from it. Calibration varies by model rather than by paradigm, so each model must be audited. Recalibration on the same labels reduces calibration error by a factor of 3.3. Agreement with coded fields understates fidelity to the narrative by a median of 0.26 in kappa. A resolution-floor bound covers any model that reports probabilities on a discrete grid. A review budget over flagged records gives the records a human must read per variable and per year. Adding the calibrated variables to the coded fields raises the injury and fatal crashes attributed to nine factors by 10,747 per year.

Let $X$ denote the number of positive integers which are a prime plus a square. We prove that $E(X)=O(X^{4/5})$.

Femtosecond laser pulses have incredible potential but still face some performance and stability issues. Here we discover a new nonlinear optical effect, frequency-comb-induced stimulated Brillouin scattering resonance, which can only be excited by a new type of soliton, adaptive solitons. Adaptive solitons possess the unique properties of adaptive down-chirp which breaks area theorem limitation on pulse energy in normal dispersion lasers, spectral profile self-regulation which provides high pulse contrast and breaks gain narrowing limitation in amplifiers, and freedom from dispersive radiation that weakens and deforms current ultrashort laser pulses in transmission media. More intriguingly, they have an adaptive transmission gain in normal dispersion waveguides which has the potential to enable them to be lossless in long normal dispersion waveguides for repeaterless soliton communication. A passive frequency-modulation mode-locked fiber laser was successfully built and generated incredibly stable adaptive solitons. Even though the laser had no negative dispersion elements, the output solitons were measured as down-chirped which enables them to keep soliton properties in normal dispersion waveguides, perfect for ultrafast applications with waveguide delivery. With the advantages of high consistency, high pulse contrast, and high energy capability; adaptive solitons are excellent for fields including micromachining, laser surgery, quantum computing, and spectroscopy.

Accurate retinal vessel segmentation is important for computer-aided ophthalmic analysis, yet thin vessels, low contrast, and severe foreground-background imbalance remain challenging for encoder-decoder networks. This paper presents U-PEN Mamba, a U-shaped retinal vessel segmentation architecture that couples progressive nonlinear feature expansion with selective state-space modeling. The proposed network enriches local vessel responses with progressive expansion, models long-range spatial dependencies through a Mamba Global Context (MGC) block with linear sequence complexity, and uses attention-based decoder fusion to recover fine vascular boundaries. We evaluate U-PEN Mamba on CHASE DB1 and DRIVE using a consistent patch-based preprocessing pipeline and compare it with convolutional, attention-based, transformer-based, and Mamba-based segmentation baselines. U-PEN Mamba obtains the best mean intersection over union among the compared methods, achieving 0.8394 on CHASE DB1 and 0.8221 on DRIVE, with Dice scores of 0.8187 and 0.8078, respectively, using 21.6M trainable parameters. Ablation studies show that the MGC block contributes the largest gain over the U-Net baseline, while projection dimension and state size provide practical accuracy-efficiency control. These results indicate that selective state-space modeling is a promising global-context mechanism for parameter-efficient retinal vessel segmentation. Code is available at: https://github.com/areyesan/UPEN_Mamba.

World Action Models (WAMs) have emerged as a promising paradigm for generalizable robot control. Despite the growing number of WAM systems, existing works often introduce unified systems that bundle together multiple design choices, such as architecture and training strategy, making it difficult to isolate individual contributions and systematically compare alternative designs. In this work, we present a controlled study that disentangles these design choices and analyzes not only their empirical effects, but also how and why they shape WAMs. More specifically, we focus on three fundamental questions in building WAMs: (1) what causal structure should govern the interaction between world modeling and action generation? (2) in which latent space should world modeling be performed? and (3) how do different world-action modeling objectives affect model behavior and performance? Through structurally controlled experiments on three representative benchmarks, RoboCasa-GR1, LIBERO, and LIBERO-Plus, we systematically compare six causal structures, eight latent representations, and four training objectives, covering popular design choices in existing WAMs. We further validate our key findings on real-robot data from the DROID dataset. We hope to provide a systematic understanding of how core design choices affect world-action modeling and what principles can guide the development of future WAM systems.

We abstract and prove some fundamental lemmas in universal blowups

Speech assessment tools for speakers with speech pathology must be both accurate and interpretable if they are to be adopted in clinical practice. Existing reference-audio measures such as the Neural Acoustic Distance (NAD) reach high speaker-level correlations with listener intelligibility scores but operate on self-supervised features that are hard to interpret, providing only frame-level explanations. We propose ART-NAD, a reference-audio intelligibility metric that replaces the wav2vec2 features of NAD with vocal-tract constriction variables (tract variables, TVs) predicted from audio by a speaker-independent acoustic-to-articulatory inversion model trained on the same wav2vec2 features. ART-NAD is computed as the multivariate Dynamic Time Warping distance between the nine-channel quasi-TV trajectories of the test and one or more references. Across 20 reference-audio protocols spanning six pathological-speech datasets and five languages, ART-NAD with silence trimming (ART-NAD-FA) reaches the same average speaker-level Pearson correlation as NAD-FA (both $r=0.71$) on the same self-supervised backbone, with no significant per-protocol difference (Wilcoxon $p=0.18$), and is the strongest reference-audio metric on 6 of the 20 protocols. Beside the score itself, each TV channel visualizes which constriction deviates from the reference over time, providing interpretable information as to where articulation breaks down.

We prove that every stable weak critical point of the self-dual abelian Yang–Mills–Higgs energy on the round three-sphere is gauge equivalent to the vacuum, for every positive scale parameter. This establishes the three-dimensional statement proposed by Cheng. For the non-stable critical point, we give a quantitative upper bound for the lowest eigenvalue of the Hessian on the gauge quotient.

The convergence of highly mobile Dirac fermions and flat-band heavy electrons offers a paradigm for emergent quantum phenomena. However, experimental realization of such intriguing state remains elusive. In this study, we report a dual carrier regime in the kagome metal Co3In2S2, wherein the charge transport is governed by high-mobility electrons while the thermodynamic responses exhibit heavy-electron behavior. This exotic duality arises from the coexistence of topological Dirac fermions and flat-band high-order (4th-order) Van Hove singularities (HOVHSs) at the Fermi surface, as revealed by magnetic-torque quantum oscillation and angle-resolved photoemission spectroscopy. The interaction between Dirac and HOVHS-derived carriers can be captured by a minimal two-pocket model, manifesting as sublinear resistivity above ~100 K and field-induced non-Fermi-liquid behavior at low temperatures. Our study establishes Co3In2S2 as a model platform for exploring many-body physics at the intersection of topology and correlation effects, and provides a foundational framework for designing quantum materials hosting diverse emergent states.

This paper is concerned with the following planar Schrodinger-Poisson system: $\begin{cases} -\Delta u +V(x)u+\lambda\phi u=u\ln u^2, & \text{in }{R}^2,\\ \Delta\phi=u^2, & \text{in }{R}^2. \end{cases}$ where $\lambda\in{R}$ is a parameter and $V\in C^1({R}^2,R}^{+})$ is a coercive potential. Due to the presence of the logarithmic nonlinearity, the manifold method developed by Ruiz [R] is not applicable here. We apply a general minimax principle to an auxiliary functional and prove the existence of a nontrivial solution. Then, by minimizing the energy functional over the set of all nontrivial solutions, we succeed in showing that the system admits a ground state solution. If, in addition, $V$ is radially symmetric, we obtain infinitely many non radial sign-changing solutions.

Edge deployment motivates forecasting models with compact parameter storage and low-bit representations. Deep equilibrium models (DEQs) obtain implicit depth by repeatedly applying a shared layer, reducing the parameter cost of explicit layer stacking. Their usual Anderson solver, however, searches for update coefficients in the continuous real domain. We propose Q-DEQ, which formulates local updates in DEQ forward solving as discrete optimization problems. Candidate directions are constructed from the current state and iteration history, and a local quadratic residual model is used to evaluate their combinations. Binary encoding of the direction coefficients yields a quadratic unconstrained binary optimization (QUBO) problem that can be solved by simulated annealing (SA) or a coherent Ising machine (CIM). After fixed-point solving, a re-forward pass applies W8A8 fake quantization to the shared layer's weights and activations. We evaluate Q-DEQ with an iTransformer backbone on five multivariate time series forecasting datasets. Relative MSE differences from the explicit multi-layer baseline range from $-1.16\%$ to $+2.90\%$, with lower MSE on two datasets. DEQ parameter sharing reduces parameter counts by factors of $1.80\times$–$3.82\times$; combined with W8A8, static weight storage is reduced by factors of $4.3\times$–$12.8\times$. Local QUBO problems solved using CPU-based SA and the Kaiwu CIM physical backend produce closely matching downstream forecasts. These results establish local discrete solving as a viable component of DEQ time series forecasting and provide a route for executing fixed-point updates through different combinatorial optimization backends.

Let $n \ge 3$ and fix $p>n$. We establish a sharp quantitative stability result in $W^{1,p}$ for Liouville's theorem for nonconstant, sense-preserving quasiregular mappings whose outer distortion $K$ is sufficiently close to one. We first reorganize Reshetnyak's classical local argument \cite{R1976}, drawing systematically on modern techniques such as those developed in \cite{FZ2022}. We then give two globalization schemes on bounded, connected domains. For bounded John domains, instead of Reshetnyak's original construction \cite{R19762}, which glues Möbius transformations on adjacent Whitney cubes, we use Whitney chains and Bojarski's enlarged-cube estimate to obtain a quantitatively sharp Euclidean stability result. Finally, we extend this idea to general bounded, connected open subsets of $\mathbb{R}^n$ via the Lorentzian representation of the Möbius group, yielding a compactified, weighted stability theorem whose underlying measure is absolutely continuous with respect to Lebesgue measure and has density bounded above by one.

Dense pass surfaces give, for every pitch cell, whether a pass played there would arrive, whether the carrier would choose it, and what the possession would then be worth. The networks that draw them read the state as a raster of per-cell counts, losing where inside a cell each player stands. LiDAR detectors, bird's-eye-view perception and graph weather models move entity features onto a grid, binning each entity to a cell or learning the transfer. We evaluate the interpolated form: each player's features are scattered bilinearly onto the grid at the player's measured coordinates, so the surface loss trains the per-player encoder end to end. Those systems adopt an interface; this paper measures one. On 53,628 passes from the 2022 World Cup, painting improves selection likelihood over the same core fed rasters alone by about a quarter of a nat: in every match of an eight-fold cross-validation, with every arm tuned over five seeds, and after retraining on seven Bundesliga and 2. Bundesliga matches from another provider. Thirteen pre-specified studies locate the gain: painting the nine raw player features with no encoder carries three quarters of it, and the learned encoder and message passing add a smaller, resolved increment. Painting also helps the original SoccerMap and a canonical U-Net, whereas offset channels, a finer raster, an attention painter and a raster-free decoder do not. Frozen across the provider boundary the likelihood advantage is lost; injected tracking error compresses it. These results concern observed-endpoint prediction, not calibrated evaluation of hypothetical passes.

Grating-based computational imaging shifts high-spatial-frequency information into the detectable range, enabling super-resolution reconstruction. However, a fixed grating produces effective diffraction-mediated shifts only for specific spatial-frequency vectors, limiting spatial-frequency coverage. Here, we propose a synthetic-aperture super-resolution method in which repeated imaging with a rotating grating broadens spatial-frequency coverage and expands the effective aperture. A physics-prior-guided restoration framework then employs a multichannel deep-learning network to fuse images acquired at different grating orientations. Using diffraction images from only three grating orientations, the proposed method reconstructed the object with a resolution of $\lambda/3.9$. This approach offers a practical route to grating-modulated super-resolution imaging in systems with limited numerical aperture.

Machine learning (ML) is expected to speed up the discovery of single-ion magnets (SIMs), but does the structural information available before synthesis allow such predictions? For 1215 lanthanide complexes from the SIMDAVIS 1.2.1 database we compared three increasing levels of structural description: tabular features of the coordination site, continuous symmetry measures of the coordination polyhedron, and the complete 3D arrangement of atoms. All three converge to an accuracy near 76%, only slightly above the 71% of the single rule "predict SIM for Dy3+". To explain the failures, we combined multireference ab initio calculations with an inspection of the structures behind the high-confidence errors. The SIMs missed by the geometric models are field-induced relaxers whose ground Kramers doublets are prone to tunnelling, a property invisible to geometric descriptors. Many false positives contain several lanthanide centers or radicals, so their relaxation is collective and outside the single-ion picture. The electronic-structure and connectivity information needed to identify SIMs is therefore not accessible to geometric methods alone. Geometric models remain useful: restricting the screening to compounds with high prediction confidence raises the accuracy to 88% while retaining 48% of the dataset. Building on the analysis of the failures, we propose a strategy that combines simple filters for nuclearity and for radicals with ligand-field descriptors from ab initio calculations.

A random group in the square model $\mathcal{Q}(n,d)$ is given by a presentation with $n$ generators and a uniformly random set of $(2n-1)^{4d}$ cyclically reduced relators of length 4 over them. We prove that if $d>\frac{5}{12}$, then a random group in $\mathcal{Q}(n,d)$ has Kazhdan's property (T) asymptotically almost surely (a.a.s.). This provides a new construction of infinite word-hyperbolic Kazhdan groups when $d\in\left(\frac{5}{12}, \frac{1}{2}\right)$. Moreover, also for $d>\frac{5}{12}$, we show that a random group in the square model a.a.s. has property $(\textrm{F}L^p)$ for an increasing range of values of $p$, and property $(\textrm{F}_X)$ for any fixed uniformly curved Banach space $X$. These results lead to bounds on the conformal dimension of the boundary of a random group in the square model. In the process we devise a method of applying the spectral link criteria for property (T), and other fixed point properties, to the groups presented by relations of length 4. In order to use it for the square model, we verify the required spectral gap hypothesis by the trace method, in the spirit of the work of Broder-Shamir.

This paper presents an LLM-based system that translates natural-language access control policies (NLACPs) into executable Rego code for Open Policy Agent (OPA). It provides a modular, end-to-end pipeline for policy detection, component extraction, schema validation, linting, compilation, and automated test generation and execution. The system is designed to bridge the gap between human-readable access requirements and machine-enforceable policy-as-code (PaC), with a focus on deployment reliability and security correctness. We evaluate the system on 372 ACRE-complete access control statements with non-null subject, action, and resource annotations against a direct single-prompt LLM baseline to isolate the contribution of structured decomposition and schema-aware validation. The system achieves a 50.3% end-to-end policy correctness rate, compared with 15.3% for the baseline, representing a 3.3x improvement. A policy is counted as correct only if it satisfies compilation, linting, and both positive and negative tests, making this a strict measure of deployable correctness. On security-critical patterns, the system generates correct deny semantics for 87.5% of deny policies (baseline: 37.5%), ownership conditions for 100% of ownership-qualified policies (baseline: 40%), and status-qualified conditions for 100% of status-qualified policies (baseline: 55.6%). These results indicate that structured decomposition and schema-aware validation play a critical role in improving the reliability of LLM-generated authorization policies.

By a result of F. R. Keogh in 1959, we have the inequality $L(r,f)/M(r,f)\le 2\pi+4\log[(1+r)/(1-r)]$ for a starlike function $f$ on the unit disk, where $L(r,f)$ and $M(r,f)$ denote the length of the curve $\theta\mapsto f(re^{i\theta})$ and the maximum value of $|f(z)|$ on the circle $|z|=r$ for $0<r<1.$ E. Crane and D. Markose in their 2005 paper showed that the constant $4$ is best possible. D. K. Thomas obtained in 1968 the inequality $L(r,f)/\sqrt{A(r,f)}\le 2\sqrt{\pi}(1+\log[(1+r)/(1-r)])$ for a starlike function $f$, where $A(r,f)$ is the area of the image of the disk $|z|<r$ under the mapping $f.$ In this paper, we extend these results to the case of $\lambda$-spirallike functions for a given $\lambda$ with $-\pi/2<\lambda<\pi/2.$

In this paper, we investigate the relation between the category of 3-crossed modules and the category of Gray-type 4-groups. The notion of a 3-crossed module was first introduced by Arvasi et al., motivated by the question of what kind of algebraic structure completely encodes a homotopy 4-type. On the other hand, from the point of view that higher groups are equivalent to algebraic realizations of higher categories – as exemplified by the relationship between 2-crossed modules and Gray 3-groups established by Sarikaya–Ulualan – it had not been clear how the 3-crossed modules of Arvasi et al. relate to any higher category. In our previous paper, we proposed a new definition of a 3-crossed module and observed that it admits a natural interpretation in terms of higher categories. In this paper, we make this interpretation precise: we introduce a 4-category, which reduces to a semistrict braided monoidal 2-category when restricted to a single object and a single 1-morphism, and prove that the category of our 3-crossed modules is equivalent to the category of Gray 4-groups, defined as single-object versions of this 4-category in which all morphisms are invertible. Furthermore, while Gray 4-groups provide a conceptual framework for 4-dimensional higher structures, they are often computationally intractable. Our equivalence establishes 3-crossed modules as a concrete, group-theoretic calculus for Gray 4-groups, providing a powerful computational tool for studying surface knots, state-sum invariants, and higher gauge theories.

Reliable action evaluation in contact-rich manipulation requires looking beyond the current observation to future visual and contact consequences. Existing noise-space reinforcement learning efficiently steers a frozen Vision-Language-Action (VLA) policy, but its critics largely ignore these consequences. We present Imagine-RL, which augments noise-space VLA post-training with action-conditioned visual-torque imagination. For each candidate action chunk, a frozen visual-torque latent world model (VTLWM) autoregressively predicts compact future representations without pixel reconstruction. A current image-state-action query attends to observed histories and predicted futures, while previous-window prediction residuals provide token-wise confidence priors that suppress unreliable future tokens. By combining current evidence with predicted consequences, the action critic better evaluates candidate actions and supervises the actor, while the VLA and VTLWM remain frozen. Across four real-robot tasks with 50 evaluation trials per task, Imagine-RL uses only 100 RL trajectories and improves the average success rate by (23.6%) over DSRL and by (60%) over VLA baselines.