Papers

Infographic generation challenges text-to-image models because a single image must satisfy numerous visual, textual, and semantic constraints. Iterative agentic refinement with a multimodal verifier is a natural remedy, but existing methods face a scale mismatch: local edits cannot correct global composition errors, while full regeneration may destroy already-correct regions. We introduce Stride, a constraint-grounded multi-agent framework that treats refinement over any frozen generator as a history-aware evolution strategy. Stride separates constraint evaluation - whether each requirement is satisfied - from visual grounding - where and how it is violated. It then routes global revisions to a composer subagent and local corrections to a retoucher subagent. Each subagent conducts internal planning and generates multiple candidates, while Stride accepts a candidate only when it improves the verifier score, reducing regression across iterations. Because stochastic generators and imperfect verifiers make any single step unreliable, it is this combination of scale-aware routing, per-step redundancy, and monotonic acceptance that yields stable improvement across iterations. With fully open-weight generator-verifier systems, Stride outperforms proprietary systems including Nano-Banana-2.0 and Seedream-5.0-Pro on BizGenEval, matches GPT-Image-2.0 and surpasses Seedream-5.0-Pro on IGenBench, and achieves a new state-of-the-art score on WISE, while substantially outperforming existing agentic methods across all evaluated benchmarks.

We describe a family of two-dimensional metric deformations that preserve integrability. The seeds are (classically) conformal integrable field theories and the deformations are directly related to different classes of auxiliary field sigma models. We introduce a master action connecting deformations by Lie-algebra-valued auxiliary fields, the so-called $\nu$-frame, to deformations by two Lorentz-charged scalars. These auxiliary scalar fields can be identified as Beltrami differentials of an auxiliary two-dimensional metric, providing a direct connection with the metric approach to $T\bar{T}$-like deformations. For Weyl-invariant seed matter theories, the auxiliary metric sector is described by a reduced gravitational potential. We show that the resulting framework preserves classical Lax integrability whenever the seed matter theory admits a Lax representation of its equations of motion on a generic curved two-dimensional spacetime. Finally, within the Lorentz-invariant family and the zweibein deformations of conformal matter theories considered here, we identify $T\bar{T}$ as the only deformation that can be interpreted as a field-dependent coordinate transformation.

Target speaker extraction (TSE) is a key frontend for enabling audio large language models (LLMs) to recognize and understand a designated speaker in overlapping speech. However, multilingual mixtures exhibit heterogeneous extraction demands, causing fixed-depth systems to either under-process challenging inputs or waste computation on inputs that have already converged. Existing TSE frontends generally apply uniform computation, while Audio-LLM adaptation methods neither explicitly model language-conditioned extraction demands nor preserve plug-and-play compatibility with frozen downstream models. We therefore propose LATTE, a lightweight 5.2M-parameter frontend that combines an acoustic Difficulty Estimator, a task-adaptive phonology-informed prior learned from multi-depth TSE gains, and an Adaptive Hourglass Extractor to route each mixture without requiring language identity at inference. On PolyExtract, LATTE achieves a macro SI-SNRi of 15.07 dB at 0.30 GFLOPs, retaining performance within 0.09 dB of a 0.53-GFLOP fixed-depth model while reducing computation by 43.4%, and lowers the average WER from 16.8% to 14.6% relative to TF-GridNet. By jointly modeling sample-level extraction demands and phonological structure, LATTE provides a practical framework for quality-aware, compute-efficient multilingual TSE and offers a scalable path toward robust Audio-LLM deployment.

The Ba-atoms in BaFe12O19 were substituted by Eu-atoms to prepare the material of composition Ba1-xEuyFe12O19. The Eu atoms occupied at the sites of Fe atoms. The atomic ratio of Eu/Ba were varied from 0 to 0.33 to control the secondary phase (hematite) and M-type hexaferrite. Raman spectra provided complimentary support for a systematic increase of the hematite phase on increasing the Eu/Ba ratio. X-ray photoelectron spectroscopy informed the presence of oxygen deficiency and surface defects, and charge state of Ba and Fe/Eu ions close to +2 and +3, respectively. The material showed direct optical transitions with band gap in the range of 2.25-3.09 eV. The increase of Eu/Ba ratio systematically increased the saturation magnetization from 84.44 emu g-1 to 57.68 emu g-1 at 3 K and 67.09 emu g-1 to 43.42 emu g-1 at 300 K, along with remarkable enhancement of the coercivity (914- 3656 Oe at 3 K and 1996-4862 Oe at 300 K). Electrical conductivity increased from 10-11-10-10 Sm-1 at 30 K to 10-5 -10-4 Sm-1 at 300 K. The electrical conductivity analysis reveals the Efros-Shklovsky-type variable-range hopping mechanism at the low-temperature region, whereas the Mott variable range hopping mechanism is applicable near to room temperature. The analysis of current-voltage characteristics provided electrode to sample interfacial barrier height of 0.27-0.74 eV. The material exhibited novel magneto-electronic properties (bi-stable electronic switching and its transformation in the temperature scale, magnetoresistance and magnetoelectric coupling) which are highly useful for spintronic devices. This work demonstrates that controlled Eu/Ba atomic ratio in the stoichiometric and non-stoichiometric lattice structure could be an effective strategy to widely tune the magnetic, optical and magneto-electronic properties in M-type Ba hexaferrite material.

3D Gaussian Splatting (3DGS) is a powerful representation for real-time neural reconstruction and rendering. While existing 3DGS systems rely on rasterization for efficiency, recent work explores ray tracing to enable secondary lighting, highly distorted cameras, and depth-of-field effects. However, compared with rasterization, ray-traced 3DGS introduces three major challenges: (1) the highly non-uniform spatial distribution of massive numbers of Gaussian primitives creates severe load imbalance; (2) neighboring pixels often generate rays with highly similar traversal paths, leading to substantial redundant traversal overhead; and (3) supporting both Gaussian and triangle primitives yields heterogeneous intersection workloads that are not well matched to existing GPU architectures. We present H2-Ray, a hybrid and hierarchical ray tracing architecture for efficient 3D Gaussian rendering. H2-Ray introduces three techniques. Load-Balanced Spatial BVH (LB-SBVH) partitions the scene into uniform grids and uses density-aware representations to convert an imbalanced global workload into balanced local traversal units. Ray-Cluster Path Reuse (RCPR) lets a proxy ray share traversal state with neighboring rays to amortize redundant traversal. The Unified Intersection Engine (UIE) supports mixed Gaussian and triangle intersections through a mode-multiplexed datapath that shares 40% of its floating-point units across both primitive types. Across 8 scenes, H2-Ray achieves a geometric-mean speedup of 3.77x and a maximum speedup of 9.26x over RaySplats on the NVIDIA RTX A5000, combining a cycle-accurate model of the modified RT Core with measured CUDA timings.

In order to control epidemics of mosquito-borne diseases such as dengue, for which there is still no vaccine available, several strategies aim to directly target the mosquito population. One technique involves introducing a symbiotic bacterium called Wolbachia into the population, which blocks the transmission of pathogens. A mathematical model of the introduction of this bacterium and the replacement of the mosquito population with a population carrying this bacterium has been developed, proving that in a homogeneous environment, there is spatial propagation of the replacement. The objective of this paper is to study the blocking of this propagation in cases where the environment is not homogeneous. In particular, we are considering scenarios where the environmental carrying capacity varies significantly across different regions of the spatial domain. To achieve this objective, we first reduce the original 2x2 reaction-diffusion system to a single closed equation, providing a simplified framework for studying the dynamics of Wolbachia propagation. We then investigate the blocking of the propagation in the population replacement process, focusing on the effects of spatial variations in the environmental carrying capacity. Numerical simulations have been performed to validate the theoretical results.

The effect of mechanical stresses and deformations upon the behavior and properties of cells and tissues is a topic of paramount interest in the field of biophysics. Its understanding is essential for deepening our comprehension of cellular responses to environmental stimuli, with implications in fields ranging from embryogenesis to tumor development. For boosting the understanding in this field, it is important to develop devices for the application of simple deformations in order to probe the cellular response to the basic mechanical transformations. While a number of stretching devices have been developed, in-plane shearing deformation has been little investigated. Here, a new device is introduced that allows the application of homogeneous in-plane shear upon a cell monolayer while imaging the sample with a commercial optical microscope. A description of the faced experimental challenges is reported and a full characterization is presented. It is demonstrated the capability of the device to apply reproducible, controlled and homogeneous shear of both single cells and confluent cellular monolayers.

Data-driven surrogates reduce the nonlinear solves required for probabilistic power flow (PPF), but models tied to a fixed bus–branch graph often generalize poorly when outages change electrical coupling. This paper proposes a topology-decomposition-driven hierarchical bidirectional graph neural network (TDD–HBGNN) for PPF under unseen topologies. For each realized topology, the network is decomposed into fundamental topological units (FTUs), dynamically homogeneous voltage clusters (DHVCs), and a core backbone sub-grid (CBSG), with equivalent-admittance representations preserving electrical ports between units. A sensitivity-based linear prior captures the first-order voltage-magnitude and phase-angle response, while the HBGNN learns topology-dependent nonlinear residuals. Impedance- and uncertainty-aware bottom-up aggregation condenses local perturbations, while mode-modulated top-down broadcasting restores system context at buses. We evaluate our approach on the IEEE 118-bus and Polish 2746-bus systems under unseen N–1 and N–2 contingencies against six baseline methods. Compared with these methods, TDD–HBGNN achieves 2.47–4.20-fold lower all-bus phase-angle errors and lower phase-angle errors in every held-out event. Its voltage-magnitude advantage is concentrated near the outaged branches, where paired error ratios reach 1.75–2.58 on the IEEE system and 1.87–1.97 in Polish N–2 events. All system–contingency–baseline comparisons favor TDD–HBGNN in joint voltage–angle error. Moreover, shared hierarchical operators keep the model size at 0.658 million parameters across both grids and yield 0.161–1.793~ms forward latency per probabilistic case. These results demonstrate system-wide angular accuracy, outage-local voltage accuracy, and parameter-efficient scaling across unseen topologies.

Existing LLM-based agent approaches for long-horizon machine learning engineering (MLE) often use context engineering, implemented through custom harnesses that manage tools, skills, and accumulated experience. However, we find that as single-session execution lengthens, the agent's reasoning intensity declines alongside slowing progress, summarized as long-horizon deceleration, and the benefits of these custom harnesses vanish as the underlying model improves, summarized as harness staleness. These findings suggest that their benefits may not persist across versions, which motivates a workflow-level approach in which agents build on one another's work across sessions. We model these alternating agent sessions as a context-reset semi-Markov decision process (CR-SMDP) and establish sufficient conditions for alternation to exceed single-agent reference limits, derive an explicit experiment-budget bound, and characterize when session caps preserve this advantage. Guided by this analysis, we introduce Humanize MLE Agents (HMA), which alternates two agents on a shared workspace, limits each session to at most k experiments and resets the context between sessions, without additional task-specific harness or prior knowledge supplements. Across 75 Kaggle tasks in MLE-bench, HMA reaches a state-of-the-art any-medal rate of 78.2%, exceeding the strongest open-source baseline by 8.0 points with a quarter of its time budget. Moreover, among six configurations spanning five heterogeneous agent pairs, HMA improves any-medal rate over the constituent baselines by 6.4 points on average, demonstrating cross-pair generality. A supplementary case on kernel optimization reaches 878 cycles, within 1.6% of the community leaderboard leader, demonstrating applicability beyond MLE.

Twisted van der Waals heterobilayers are a promising material platform for studying collective exciton many-body phenomena, but near-aligned structures often exhibit a local, anisotropic atomic reconstruction that compromises lateral homogeneity. The present study describes how atomic-scale rearrangement in adjacent regions of hBN-encapsulated, near-aligned MoSe$_2$/WSe$_2$ heterobilayers is controlled by the presence of a mono- or bilayer hBN spacer between the two monolayers. High-angle annular dark-field STEM directly resolves the atomic alignment in both layers and shows that the spacer suppresses the reconstruction and strongly increases the structural uniformity of the heterobilayers. 4D-STEM quantitatively maps local rotation, dilation, and heterostrain, revealing that the separated regions remain consistent with rigid moiré superlattice simulations, whereas without the spacer the structural parameters have two to three times broader distributions. By suppressing reconstruction, ultrathin hBN spacers therefore provide an effective route to enhance lattice homogeneity in MoSe$_2$/WSe$_2$ heterobilayers targeting collective excitonic and optoelectronic phenomena.

We present an empirical calibration of the effective spectral resolution of the JWST NIRSpec PRISM disperser based on a large sample of galaxies drawn from archival observations. Our sample spans a wide redshift range, $0.5 \lesssim z \lesssim 10$, enabling a wavelength-dependent characterization of the PRISM resolving power across the full bandpass using the [O III]$\lambda\lambda4959,5007$ doublets. To ensure robust measurements, we impose strict signal-to-noise requirements on both continuum and emission-line detections. Emission-line profiles are fitted with multi-Gaussian models, and the full width at half maximum (FWHM) is measured for each source. The derived empirical resolution curve shows a systematic offset from the nominal pre-launch estimate, lying between the tabulated instrumental resolution and the point-source shutter limit. We also discuss how source size affects the final spectral resolution, and provide an analytical formula that combines wavelength and morphology dependence in a root-sum-square framework. This work delivers a population-averaged, statistically robust calibration of the effective PRISM spectral resolution for typical galaxy observations. The resulting calibration is directly applicable to statistical analyses of galaxy spectra obtained with NIRSpec PRISM. Our empirical calibration exceeds the pre-launch JDox values by a factor of 1.03 to 1.63, depending on source morphology, and provides the first wavelength and morphology dependent calibration of the NIRSpec PRISM spectral resolution.

Recent advances in large language models (LLMs) have enabled agent-based approaches for repository-level automated vulnerability repair (AVR), showing promising repair capabilities. However, an important issue has received limited attention: how can we ensure that the evidence generated during the repair process is reliable enough to support accurate vulnerability understanding and patch generation? In this paper, we propose EviRepair, an evidence-driven multi-agent framework for repository-level AVR. EviRepair introduces evidence review into the repair process by enabling agents to collaboratively collect vulnerability evidence, verify evidence consistency, and construct a reviewed vulnerability model for patch synthesis and validation. Extensive experiments on PatchEval and SecBench benchmarks with multiple agent frameworks and LLMs demonstrate that EviRepair consistently outperforms existing agent-based baselines, achieving average improvements of 16.37% and 40.33% in resolved rates on PatchEval and SecBench, respectively. Codes are available at https://github.com/lly-s/EviRepair

Following \cite{BR} we study hyponormal operators in the strictly larger class $\beta(H)$ of operators whose restriction to every non-zero reducing subspace is norm attaining. The Weyl-type characterization of positive operators via the essential spectrum used in the absolutely norm attaining case is replaced by a well-ordering condition on the eigenvalues (Theorem~\ref{thm:positive}). We prove a transfinite, block-diagonal representation $T=\bigoplus_i\lambda_iS_i$ (with isometries $S_i$) for the $\beta(H)$-operators whose $|T|$-eigenspaces are reducing, equivalently the quasinormal operators with $|T|\in\beta(H)$, and we show by examples that hyponormality alone does not give such a decomposition. For normal operators we obtain a complete representation, and for hyponormal $\beta(H)$-operators we show that normality is equivalent to the spectrum having planar Lebesgue measure zero. An analogous area-zero criterion for normality is proved for hyponormal operators attaining the minimum modulus on every non-zero reducing subspace.

This paper considers the problem of estimating the ratio of variance components of a balanced one-way random effects model. Existing estimators of ratio of variance, such as the ANOVA and maximum likelihood estimators, can take negative values and are inadmissible under quadratic loss. We therefore study the problem under a general class of scale-invariant loss functions. We characterize the class of scale-equivariant estimators of ratio of variance and obtain the best equivariant estimator. We then derive a class of estimators that dominate the BEE and extend this class to obtain further improved estimators. We propose a smooth improved estimator of ratio of variance. For interval estimation of ratio of variance, we derive an asymptotic confidence interval, bootstrap confidence intervals, a generalized confidence interval and a highest posterior density credible interval. The performance of the proposed improved point estimators and confidence interval procedures is assessed through an extensive simulation study. Finally, we provide a real data analysis for implementation purposes.

A pair of topological spaces $X$ and $Y$ is a Fourier–Mukai (FM) pair if there is an equivalence of $\infty$-categories of derived sheaves of abelian groups \[\operatorname{Shv}(X;\mathrm D(\mathbb Z))\simeq \operatorname{Shv}(Y;\mathrm D(\mathbb Z)).\] An FM pair $(X,Y)$ is non-trivial if $X$ and $Y$ are not homeomorphic. We consider the question of whether non-trivial FM pairs $(X,Y)$ exist for which $X$ and $Y$ are both "nice" spaces, which in this article means admitting a triangulation. We show that the answer is no if $X$ is second-countable and either (i) one-dimensional, (ii) a surface, or (iii) the 3-sphere. In order to prove this, we define two invariants of dualizable categories. The first invariant is an extension of Tate–Hochschild cohomology (aka singular Hochschild cohomology) to a class of dualizable categories satisfying a countability assumption. For a homology manifold $X$, we relate the Tate–Hochschild cohomology of $\operatorname{Shv}(X;\mathrm D(\mathbb Z))$ to the homology at infinity of $X$ (in the sense of proper homotopy theory). The second invariant takes the form of a subcategory $\mathcal D_{\mathrm{Gor}}\subseteq\mathcal D$ called the Gorenstein locus, defined for every dualizable stable category $\mathcal D$. For a triangularizable space $X$ and a field $k$, we show that the Gorenstein locus of $\operatorname{Shv}(X;\mathrm D(k))$ is equal to the full subcategory of sheaves supported on the $k$-homology manifold locus of $X$.

In a Latin square, every row can be interpreted as a permutation, and therefore has a parity (even or odd). We prove that in a uniformly random $n\times n$ Latin square, the probability that all rows are even is of the form $2^{-n+o(n)}$. This fills a gap left by recent work of Kwan, Petrova and Sawhney: they proved that the row parities behave like a sequence of independent coin flips in a variety of different senses, but they were not able to lower-bound the all-even probability, as their approach had a small number of "exceptional rows" whose parities they could not control. In fact, we prove a more general theorem on the probability of any possible prescription of row parities, column parities and symbol parities. Our approach extends the ideas of Kwan, Petrova and Sawhney, introducing a new way to "bootstrap" intercalate switchings to control more complex switching operations.

Consider \begin{equation*}\ \left\{ \begin{aligned} -\mathcal_{\lambda,\Lambda}^{+}(D^{2}u)&=\mu u+a(x)u^{p}\quad\text{in}~\Omega,\\ u&=0\quad\text{on}~~\partial\Omega, \end{aligned} \right. \end{equation*} where $ \ Omega$ is a smooth bounded domain, $a$ is a continuous function which is allowed to change sign. Moreover, the set of zeros of $a$ may have a non-empty interior. The main objective of this article is to establish a uniform bound on the set of positive solutions of the above problem. This approach requires a suitable Liouville-type theorem. We first prove the Liouville-type theorem for $-\mathcal_{\lambda,\Lambda}^{+}(D^{2}v)=h(x_{1})f(v),$ where \(h\) is a strictly increasing one-dimensional weight and \(f\) is positive and nondecreasing.

Agentic orchestration delegates tasks to sub-agents with independent contexts, providing a key path to extending the effective execution horizon of large language model agents. However, existing orchestration methods face two limitations: in execution, current methods fix sub-agents' goals and harnesses at creation time, limiting their adaptability to dynamic real-world environments; in optimization, sparse and delayed feedback constrains effective learning of the orchestration policy. To address these limitations, we introduce POrchestra, an on-the-fly proactive agentic orchestration framework. It allows sub-agents to proactively communicate with the orchestrator at any logical point to request harness adjustments while maintaining continuity of local execution. This mechanism not only enables sub-agents to adapt seamlessly to dynamic environments but also naturally inspires On-Policy Orchestration Distillation (OPOD) based on hindsight feedback. OPOD attributes sub-agents' proactive revision requests back to preceding orchestration decisions to derive targeted improvement signals, and leverages these signals as process supervision alongside the final reward to optimize the orchestration policy. We evaluate POrchestra on three long-horizon agent benchmarks spanning deep research, dynamic digital assistance, and software engineering. POrchestra improves task success by an average of 9.1% relative to the strongest baseline; combined with OPOD, it improves small-orchestrator success by an average of 10.0% relative to existing training baselines. POrchestra also achieves a more favorable cost-performance trade-off. Our code is publicly available at https://github.com/XueyangFeng/POrchestra.

We prove the Berezinskii-Kosterlitz-Thouless (BKT) phase transition in the large-distance behaviour of the two-point correlation function of the $\mathsf{Sine}_\beta$ point process for all $\beta>0$, confirming the first term of an asymptotic expansion predicted by Forrester.

In this paper we propose a novel regularisation strategy for structured linear inverse problems of the form $Ax=F \circ G x = z$. Instead of using the operator $A$ or a complex scheme involving both $F$ and $G$ simultaneously, combining already existing and simpler regularisations for $F$ and $G$ allows the use of established and optimised programs for high-speed computations. As classical parameter choice rules fail in the scenario when no source conditions are known because intermediate error bounds may be unavailable, we provide both a-priori and a-posteriori rules with a convergence speed analysis given source conditions. We test the proposed method on the pre-clinical medical imaging technique of magnetic particle imaging with different choices of regularisation and on a convolution problem for an analysis of the convergence speed.

When investigating the performance of supercapacitors (SCs), it was found that they offer high-power density and long life but are limited in capacity and energy density. Water-in-salt electrolytes, i.e., 21___m lithium bis(trifluoromethanesulfonyl) imide (LiTFSI), offer a solution by expanding the electrochemical window compared to a diluted aqueous environment. While significant research has been dedicated to improving these electrolytes, the impact of carbon properties on energy storage remains relatively underexplored. This study investigated the influence of carbon structures, defects, and surface functional groups on supercapacitive performance in LiTFSI electrolytes. For this purpose, a series of carbon materials, including carbon nano-onions and porous conductive carbon black (ENSACO), were synthesized and systematically modified by oxidative and reductive thermal treatments. Our results indicated that higher specific surface area and active surface area improve the ion adsorption and capacitance, while specific oxygen functionalities, such as carboxylic and anhydride groups, were found to significantly enhance capacitance. Furthermore, crystallinity and graphitic characteristics play a role in capacitance, with smaller graphene domains and greater disorder promoting ion storage. The study demonstrates a direct correlation between carbon microstructure and electrochemical behavior, providing insights into the rational design of carbon electrodes in high-performance SCs.

On-policy distillation (OPD) provides teacher supervision on student-generated trajectories, but a single trajectory realizes only one continuation at each decision, limiting supervision coverage under a finite sampling budget. We propose BranchOPD (Branching On-Policy Distillation), which selects informative decision points using student uncertainty and teacher-student disagreement, resamples student-policy continuations from shared prefixes, and applies token-level teacher supervision to both main trajectories and branches. BranchOPD operates at token-level decisions in mathematics and within-turn decisions in agent tasks. Shared-prefix reuse reduces student-generated token costs by approximately 19% on ALFWorld and 31% on WebShop relative to seven independent trajectories. We also introduce protocol-boundary repair (PBR), which uses targeted supervision under protocol constraints to mitigate repetition and wasted generation. BranchOPD outperforms Vanilla OPD and Multi-Rollout OPD (n=7) across all evaluated benchmarks, with gains over Vanilla OPD of 18.55 percentage points in mean mathematics accuracy over 16 sampled answers (avg@16) and 13.8 points in mean ALFWorld ID/OOD success. Mechanistic analyses and selection ablations show that branching at uncertain decisions expands subsequent behavior coverage and outperforms random selection and turn-initial branching.

Nonlinear model predictive control (NMPC) can be applied to large nonlinear systems with complex objectives while enforcing constraints, but the cost of solving the underlying optimization problems limits real-time application for systems with fast dynamics or many states. Neural networks can reduce this online cost by approximating the control law, but may violate constraints and typically require many precomputed optimizer solutions for training. The learning-based iterative solver for constrained optimization (LISCO) instead learns to predict primal-dual steps toward satisfaction of the Karush-Kuhn-Tucker (KKT) conditions through self-supervised training without precomputed solutions, but its dense, monolithic architecture grows with the prediction horizon. We remove this horizon dependence by exploiting the temporal structure of the problem in the solver architecture, which makes the network size independent of the horizon while leaving the training loss and the solver iteration unchanged. A closed-loop resampling strategy further aligns the training distribution with closed-loop operation at no additional sampling cost. On an economic NMPC benchmark of a CSTR cascade, the proposed solver scales to larger problems than monolithic LISCO and achieves median speedups of up to a factor of four over IPOPT. In closed loop, it achieves comparable control performance to IPOPT with no observed constraint violations.

Generating edge case scenarios is crucial for training, testing and safety assuring autonomous systems. This identifies hazardous failures to increase system reliability and robustness, ensures the system can still function safely on the boundaries of its operational design domain and learns the expected system behaviour for these edge cases. The rapid advancement in the generation and analysis capabilities of language models (LMs) has expanded their applicability and recent work has investigated LM scenario generation. However, many recent approaches rely on human-in-the-loop or rule-based strategies. This restricts the LM's ability to generate diverse and edge case scenarios; the long tail of the distribution. Our work uses local LMs in a laptop-based agentic AI framework for adaptive scenario generation. This is cheap, fully-controlled, ensures data privacy and security. It uses think, act, observe, update, and continue loops with lightweight JSON encoding to generate scenarios. We use the system requirements, system description and environment description as knowledge bases in contextual prompts for an LM to ensure scenario realism. A second, independent LM critiques each scenario using domain specific criteria so it can be refined. The refined scenarios are run in simulation and evaluation metrics collected. These metric scores are analysed and similar scenarios are created for edge cases (exploitation) or novel scenarios are generated to explore the scenario space. Post-hoc clustering using metric scores and thematic-type analysis of the rich-text scenario descriptions produced by the LM pinpoints functional gaps and their triggering conditions. This creates traceable evidence for the safety assurance case. Our work highlights the potential of a flexible and adaptive local agentic AI framework for automating edge case generation and producing traceable safety assurance evidence.

Let $\Omega$ ___ C n be a bounded hyperconvex domain and $\Phi$\,: $\Omega$ $\rightarrow$ R a maximal plurisubharmonic function in $\Omega$ (possibly unbounded). We introduce a new class E 1 $\Phi$ ($\Omega$) of plurisubharmonic functions with boundary values equal to $\Phi$ in the sense of Cegrell and finite $\Phi$-energy on $\Omega$. Then given a Borel measure $\mu$ on $\Omega$, we apply a variational approach to prove that $\mu$ is the Monge-Ampère measure of a function u $\in$ E 1 $\Phi$ ($\Omega$) if and only if it satisfies the integrability condition We also establish a quantitative version of this condition extending previous results of Cegrell and others. Using a logarithmic transformation, we obtain analogous results for the real Monge-Ampère equations with (unbounded) boundary data.

We derive approximation rates for Sobolev functions defined on the complex unit sphere and complex projective space, representing quantum states, and on the special and projective unitary groups, representing quantum unitary operations. By using harmonic analysis on compact groups and compact homogeneous spaces, we characterize the corresponding Peter–Weyl decompositions and Sobolev spaces via irreducible representations and the Laplace–Beltrami operator. Combining spectral truncation with finite-depth quantum-circuit approximation, invoking the Solovay–Kitaev theorem, we establish quantitative rates that separate the spectral truncation error from the circuit approximation error.

Representational similarity measures (RSA, CKA, Procrustes) are chosen for the transformations they treat as irrelevant, and all of them take the set of conditions as given. That set is fixed by two decisions, which inputs are admitted and how they are grouped, both taken before the matrix a measure operates on exists: no invariance property reaches them. We measure what they are worth where the arrangement the conditions ought to have is known independently of the systems compared, the acoustic organisation of vowels, across fifteen languages and twenty-seven representations. Changing which categories are compared, at a fixed number of them, moves the gap between two representations by more than twice the effect being measured, while changing how many moves it not at all. In this setting rankings of models are identified under these choices, and rankings across languages are not.

We prove that each simplex in $\mathbb{R}^4$ contains a point with at least $14$ emanating normals to the boundary. Earlier, the authors proved that each generic simple polytope in $\mathbb{R}^4$ contains a point with at least $12$ emanating normals to the boundary. This problem belongs to a piecewise linear counterpart of a longstanding problem concerning normals to smooth convex bodies.

Modern attention workloads require diverse masking patterns whose boundaries depend on runtime metadata, yet efficient attention kernels natively support only a small set of patterns. Existing methods for supporting custom masks in these kernels face an expressiveness-efficiency trade-off. Predicate-based methods are expressive but incur substantial preprocessing and execution overhead, whereas interval-based methods execute efficiently but restrict expressiveness through a predefined interval count. We present CompileMask, which addresses this trade-off by connecting expressive mask specifications with efficient attention execution. We design a compiler that analyzes visibility rules during the offline stage and generates a mask-specific preprocess kernel. We further propose MaskSpec, a region-based DSL that lets users express these rules. During the online stage, the generated kernel reads batch metadata and produces a compact Execution Descriptor that lets the attention kernel efficiently check visibility by comparing element indices against precomputed endpoints. Experiments show that CompileMask achieves up to $3.8\times$ speedup over state-of-the-art methods.

We consider the reachability problem in fully dynamic directed planar graphs: the graph undergoes edge updates (insertions and deletions) and we receive queries asking if one vertex is reachable from another. The current-best online algorithm for dynamic planar reachability spends worst-case time $\widetilde{{O}}(n^{2/3})$ per query/update [Subramanian, ESA '93]. This can be improved to $\widetilde{{O}}(n^{1/2})$ in the offline setting or when the embedding is fixed [Diks and Sankowski, ESA '07]. Our contribution is twofold: 1. We present the first algorithm that breaks the square-root barrier for dynamic planar reachability in the offline setting, obtaining time ${O}(n^{0.49})$ per query/update. This shows that the problem is easier than answering distance queries in a dynamic undirected planar graph, for which a conditional lower bound of $n^{1/2 - o(1)}$ is known [Abboud and Dahlgaard, FOCS '16]. Notably, this lower bound applies to both online and offline algorithms. 2. Second, in the general online setting we design a randomized data structure with amortized update and query time ${O}(n^{0.664})$. This is the first improvement upon the exponent $2/3$ in over three decades. The main engine behind our theorems is a new sparsification framework aimed at maintaining information about reachability. Specifically, we study digraphs through the lens of VC dimensionality of certain set systems. First, we design sparse reachability emulators for planar digraphs that preserve the VC dimension. Second, we utilize orderings with a low “stabbing number” [Chazelle and Welzl, Discrete Comput. Geom. '89] to compute subquadratic reachability emulators in subquadratic time whenever the VC dimension is bounded.