Papers

Cosmological first-order phase transitions can generate curvature perturbations through inhomogeneous quantum tunneling, as studied previously on superhorizon scales. In this work, we for the first time conduct three-dimensional lattice simulations that incorporate scalar metric perturbations and radiation perturbations, covering a range from bubble wall scales to super-horizon scales. We obtain the precise scalar perturbation power spectrum and the probability density function of energy density perturbations. Furthermore, we simulate the gravitational-wave energy spectra generated by each source during the first-order phase transition, including the scalar field itself, scalar metric perturbations, and the energy density and velocity perturbations of radiation. For gravitational waves, the contribution from other sources can exceed $1/3$ of that from the scalar field at superhorizon scales. Additionally, we compare the effects of different values of the transition strength and rate on the results. This paper provides more accurate numerical results for research aimed at detecting or constraining first-order phase transitions via gravitational waves and curvature perturbations.

Random projection is a preprocessing technique for optimization that reduces the number of linear equality constraints by replacing them with random linear combinations while approximately preserving the optimal value. In this paper, we emphasize the role of suprema of random processes, and in particular generic chaining, in explaining this phenomenon. By combining Lagrangian duality with generic chaining, we obtain shorter proofs and sharper guarantees that apply beyond the typical polyhedral settings based on the Johnson–Lindenstrauss lemma. More importantly, this perspective allows us to extend random projection to problems with linear inequality constraints. Although randomly projected inequality constraints generally define neither a relaxation nor a restriction of the original feasible region, we show that random projection can nevertheless approximately preserve the dual bound. The key is a new construction for randomly projecting dual certificates that preserves dual feasibility and differs from existing constructions motivated by the Johnson–Lindenstrauss lemma.

Constellation Monte Carlo results depend on the orbital population used to evaluate a tasking policy. With scarce reference trajectories, replay limits geometric diversity, while independent orbital-element jitter can violate physical constraints. We study constrained diffusion for orbital-population augmentation. A force-conditioned diffusion model learns a 13-dimensional orbital prior, recovering semimajor axis from perigee altitude and eccentricity; Basilisk propagates each sample under one of five force-model tiers. Using 800 reference trajectories, we compare diffusion with jittered bootstrap, per-tier Gaussian mixtures, and a conditional variational autoencoder, and evaluate distributional fidelity, support shift, classical astrodynamics diagnostics, and 4,000 paired GoDSAT-compatible campaigns. The largest diffusion model achieves held-out trajectory MMD of 0.0171 +/- 0.0239, similar to bootstrap (0.0170) and the mixture (0.0198), but samples farther from training priors (median nearest-training distance 2.7 versus 0.10 standardized units). All generators fail to match the shifted-blind population (classifier AUC 0.991-0.998). Endpoint-conditioned samples satisfy Lambert boundaries but have greater interior error than the matched Lambert reference (29.2 versus 5.7 km mean RMSE). Residual diffusion improves selected sparse forecasts and catalog-mode recall but does not outperform classical estimators on custody ranking. In a fixed 16-satellite configuration, diffusion yields similar mean custody to replay and bootstrap, while the force-tier mixture shifts custody by about 5.5 percentage points. Constrained diffusion supports local, in-support augmentation but cannot replace orbital dynamics or serve as an operational posterior. Orbital-population construction is a consequential source of uncertainty in constellation analysis.

We present a comparative analysis of two open-source quantum network simulators, QuISP and SeQUeNCe, focusing on cross-validation of basic networking tasks to ensure consistency and accuracy in simulation outputs. Although both simulators are designed to study quantum network management policies and their dynamics under complex noise models, their differing underlying assumptions can lead to variations in simulation results. We highlight the discrepancies in how the two simulators handle connections, internal network node processing time, and classical communication, resulting in significant quantitative and qualitative differences in the time required to perform basic network tasks such as entanglement generation, purification, and swapping. We simulate common scenarios between the simulators to compare both the latency of resource distribution and the fidelity of the distributed resources. Our findings indicate that while the simulators differ in the time required to complete network tasks—a constant factor difference attributable to their respective connection models—they agree on the fidelity of the distributed resources under identical error parameters. This work demonstrates a crucial first step towards enhancing the reliability and reproducibility of quantum network simulations, as well as leading to full protocol development. Furthermore, our benchmarking methodology establishes a foundational set of tasks for the cross-validation of simulators to study future quantum networks.

Speech Language Model (SLM) performance often degrades on dialects due to data scarcity. Conventional text-to-speech (TTS) augmentation struggles to cover diverse dialects as it requires a certain amount of real dialect speech. We propose synthesizing pseudo-dialect speech by converting LLM-generated dialect text via a standard-language TTS model, requiring zero real dialect speech. Additionally, we introduce intermediate standard-text prediction during training, acting as semantic normalization for downstream tasks. We evaluate dialect understanding via dialect-to-English speech translation across Japanese, German, and Chinese dialects. Compared to synthetic standard speech baselines, pseudo-dialect augmentation improves scores for Japanese (from 25.38 to 26.24) and German (from 31.57 to 32.47). Furthermore, the intermediate standard-text prediction effectively bridges the semantic gap, boosting performance to 28.26 for Japanese and from 11.67 to 16.37 for Chinese. These results suggest that our approach scales to various languages without requiring speech resources specific to each dialect.

By defining notions of similarity between collider events, metrics give rise to event manifolds with nontrivial geometric structure. Understanding these structures and their relation to the underlying physics remains largely unexplored, partly due to the challenge of systematically comparing spaces endowed with distinct metrics. We introduce the multi-reference relative representation (M3R) framework, which provides a unified coordinate system for analyzing different spaces on equal footing. Applying M3R to three physically motivated event metrics—the phase space, spectral 2-Wasserstein, and energy-flow 2-Wasserstein metrics—we study individual event manifolds and the decision boundaries separating different physical processes. We find that these metrics resolve distinct yet partially shared structures, while intra- and inter-manifold geometries exhibit qualitatively different properties. Combining multiple metrics further reveals complementary information that can be exploited within a unified representation. More broadly, M3R provides a general language for comparing and composing different notions of event similarity, opening a path toward a systematic geometric description of collider event space.

We study reconstruction of graded surfaces with stops $(S,M,\eta)$ from their mapping class groups and the derived Picard groups of their partially wrapped Fukaya categories. In genus at least two, we prove that the ungraded mapping class group determines the surface with stops $(S,M)$, while the derived Picard group with the shift distinguished determines the underlying graded surface $(S,\eta)$. Nevertheless, the derived Picard group with both the shift and the Serre functor distinguished has countably infinite fibres. We also construct arbitrarily large finite families of pairwise non-equivalent categories with the same invariant and Grothendieck rank. For line fields induced by nowhere-vanishing vector fields, we show that the rational Serre representation determines the surface with stops $(S,M)$ in every genus. For arbitrary line fields in genus at least two, the full integral derived Picard representation, with the shift distinguished, has fibres of cardinality at most four. It completely determines the graded surface with stops $(S,M,\eta)$ when $S$ has one or at least five boundary components, while non-singleton fibres occur for two, three, and four boundary components.

In music beat tracking, model-predicted activations must be decoded into a discrete, musically coherent event sequence. Direct peak picking closely follows local evidence but can retain spurious peaks or miss weak beats. Dynamic Bayesian networks (DBNs), a widely used structured post-processor, improve sequence consistency under predefined global tempo, meter, and transition constraints, but their behavior can depend strongly on these settings. We introduce CASM, a context-aware semi-Markov decoder that instead conditions its temporal constraint on local activation evidence. CASM also accounts for ambiguity among competing periodic interpretations, including half- and double-tempo alternatives. Deterministic safeguards prevent implausible outputs and preserve beat-downbeat consistency. Applied to fixed activations from three neural beat trackers (BeatThis, MSCNN, and TCN), CASM improves temporal continuity while preserving event-level F1 across the GTZAN and SMC datasets, without backbone retraining or dataset-specific retuning. Further analysis shows that CASM is less sensitive than the DBN baseline to the composition of the calibration data.

Synthetic aperture radar (SAR) and electro-optical (EO) imagery provide complementary observations: SAR enables day-and-night, weather-resilient sensing, whereas EO provides rich appearance and fine-grained semantic cues. We introduce SAREO-FM, which avoids forcing a single token stream to serve two distinct roles: modality tokens preserve how each sensor observes the scene through masked reconstruction, while learnable semantic queries capture what the scene contains under guidance from a pretrained vision foundation model (VFM). By jointly encoding these queries with SAR and EO tokens, the queries acquire modality-grounded semantic context, while the modality-token outputs remain the explicit targets of masked reconstruction. This design assigns semantic and reconstruction supervision to separate token streams while preserving their interaction within the shared encoder. Pretrained on the million-scale SAR-1M corpus, SAREO-FM achieves strong unimodal transfer for both SAR-only and EO-only inputs, while delivering substantial gains from joint SAR–EO observations on tasks that benefit from complementary sensing.

Let $G$ be a simple graph with cover ideal $J(G)$ in a polynomial ring $S = \k[x_1, \ldots, x_n]$. For each integer $t \ge 1$, let $\alpha_t(G)$ denote the maximum size of an ordered matching $M$ of $G$ with alternating path length $\ell(M) \le 2t - 1$. Hang, Tam, and Vu established that \[ \operatorname{depth}\!\left(S/J(G)^{(t)}\right) \le n - 1 - \alpha_t(G) \] for all $t \ge 1$, where $J(G)^{(t)}$ is the $t$-th symbolic power of $J(G)$. In this paper, we introduce a natural hereditary class of graphs $\mathcal{P}_\k$ for which this inequality holds with equality for every $t \ge 1$. We prove that $\mathcal{P}_\k$ contains all distance-hereditary graphs, and we show that within the class of chordal graphs, $\mathcal{P}_\k$ coincides with the class of distance-hereditary (or gem-free) graphs.

This paper presents an open-sourced MATLAB simulation and analysis platform dedicated to legged climbing robots. This simulator enables the design of any limbed robotic system as an articulated multi-body with a floating base and simulates it walking and climbing in an arbitrary environment. The main variable environmental parameters are inclination, gravity, and ground stiffness, and any point cloud can be installed as the terrain map. Furthermore, the simulator employs a rigid body dynamics engine. This paper first describes the simulator structure, and the computational flow and next presents the representative simulation examples where quadrupedal robots assumed gripping on the wall or climbing on the steep slope.

We propose a new variant of Vaught's conjecture, based on Martin's (model-theoretic) conjecture and the $\omega$-Vaught's conjecture of Gonzalez and Montalbán. For $\omega$-stable theories, we prove the conjecture by analyzing in detail Bouscaren's and Shelah-Harrington-Makkai's proofs of Martin's conjecture and Vaught's conjecture, respectively, for $\omega$-stable theories. In particular, when there are countably many countable models, we improve the required number of quantifiers for a Scott sentence from $\omega+\omega$ to $\omega+5$, and we obtain a similar bound of $\omega+6$ for the uncountable case.

Vision-language models (VLMs) often miss small objects in large images. We ask three questions: what limits them, which of these limits better models can remove, and whether the classical way of handling large images, local decomposition, still has a future. We answer them with a theory built on two quantities of the image interface: S, the number of visual tokens across an object's side, and L, the content a call must cover. The limits: a W x H image sent whole within N tokens gives an object of side m at most m*sqrt(N/(WH)) tokens per side. Doubling the token budget N therefore raises the largest S a whole image can reach by only 41%, and seeing an image at the S an object needs costs at least order S^2 tokens whatever the model. If recognition improves gradually with S, any search strategy, zoom agents included, obeys a recall-cost frontier. What better models can change: the S an object needs and how much one call can carry, measured in bits per object found; the coverage cost remains. Decomposition: yes. Assuming only that more tokens per object and less content per call do not hurt on average, splitting an image cannot lower expected recall if no view zooms out relative to the whole image and views overlap by one object. Neither part can be dropped; we bound the cost of every such decomposition, and a simple rule approaches the bound as the image grows. We test the theory in about 177,000 requests on 797 images. On controlled images, none of 40 orderings predicted for 8 VLMs is violated. Checked after the fact on drawings, floor plans, natural and synthetic images, 61 of 89 implied orderings hold significantly and 4 fail, all for OpenAI models given more pixels than their default path. On construction drawings the rule never significantly lowered recall relative to the whole image and raised it by up to 0.28. Code and data: https://github.com/shijunzhe/vlm-small-objects

We prove that every cluster monomial of type $A_n$ is log-concave and unimodal with respect to its Laurent expansion in a fan initial cluster. We derive a coefficient formula for laminar interval products arising from compatible diagonals in the polygon model. In even rank, we reduce log-concavity in fan coordinates to log-concavity along integer lines. In odd rank, we use convolution to handle the coefficient sums arising from the fan substitution. This gives partial affirmative answers to the log-concavity conjecture of Chen-Huang-Sun and the unimodality conjecture of Chen. Our result also complements Shen's study on the supports of products of canonical basis elements for cluster X-varieties of type $A_n$.

Diffusion language models (DLMs) generate text through iterative parallel refinement, offering the potential for higher throughput than autoregressive (AR) decoding. However, most DLMs still maintain one generative state per token, so every denoising step processes a state sequence as long as the output sequence, limiting the throughput gains from parallel generation. Continuous DLMs provide an additional degree of freedom: a single continuous state can represent multiple tokens, allowing diffusion to operate on a much shorter latent sequence. We introduce Branching Latent Diffusion (BLD), which exploits this flexibility by compressing a 1024-token sequence into only 64 block latents, a $16\times$ reduction. BLD combines latent compression with branching token realization, where each latent is decoded by a local AR branch and all branches run in parallel. Because strong compression makes joint latent generation difficult, BLD generates the latents in groups, conditioning each group on previously generated latents. In end-to-end evaluation on the same GPU, BLD reduces generation FLOPs by more than $80\times$ and increases throughput by more than $6\times$ relative to the similarly sized ELF-L baseline. Compared with the AR baseline, BLD achieves more than $6\times$ higher throughput and more than $4\times$ lower latency. Despite the compression, BLD maintains competitive local fluency and diversity, although long-range coherence remains challenging. Overall, BLD shows that moving diffusion from token-level states to compressed latent sequences can substantially improve the efficiency of long-sequence generation.

How can structured transformations of data improve regularizer design for inverse problems? We address this question through anisotropic dilation, a direction-preserving map that rescales each point along its Euclidean ray by a positive profile on the sphere. Our analysis builds on a characterization of optimal regularizers within a broad Gibbs class, where the regularizer best matched to a distribution $P$ is determined by a direction-dependent radial summary statistic $\rho_P$. We show that anisotropic dilation acts explicitly and transitively on the space of radial summary statistics: any prescribed optimal regularizer in this class can be obtained by transforming an admissible source distribution using a single explicit profile. We characterize the resulting distributional orbits and establish conditions under which this control of regularizer geometry yields a weakly convex denoising formulation even when the original objective is not weakly convex. We also derive in closed form the profile that optimally adapts a fixed base regularizer to data. Its improvement over isotropic rescaling with respect to KL divergence is governed by a Jensen gap, for which we establish strict positivity under explicit conditions for several natural families of distributions. For jointly learning the base regularizer and anisotropic profile from samples, we establish finite-sample generalization bounds, with explicit rates when the logarithm of the profile is parameterized by linear feature models or sparse ReLU networks. Experiments on a controlled two-dimensional family and on MNIST denoising demonstrate that learning the anisotropic profile can improve reconstruction performance for both handcrafted and learned base regularizers.

Generative world models provide rich predictions of how manipulation scenes may evolve toward task objectives, yet those futures do not directly expose the compact task variables required by control. When training supervises future prediction alone, terminal goal accuracy is not an explicit learning objective, even when geometric recovery is available. We present Entity-Level Goal Readout, a learned prediction-to-execution interface that makes the executable terminal goal an explicit output of a 3D trace world model. It combines object-centric pose prediction with translation grounded in observed depth to produce a compact goal in SE(3). A shared Pose-Native Executor consumes this fixed goal with online object-pose feedback for closed-loop control without rerunning the world model. Across five manipulation tasks, the pipeline achieves a mean success rate of 79.69%. Goal diagnostics directly measure terminal goal accuracy, while controlled translation perturbations characterize how execution degrades under goal error. Zero-shot deployment on a Franka arm achieves 73.33% success on nominal StackCube, 66.67% with distractors, and 75.00% on PickPlate with a target unseen during policy training. These results support treating the prediction-to-execution interface as an explicit learned component of world-model planning rather than incidental post-processing in the control pipeline itself. Project page: https://claire0730.github.io/executable-goals/

REBCO coated conductors have been used in ultrahigh field magnets for condensed matter physics research, nuclear fusion, particle accelerators, and NMR applications. It is well known, however, that they are not mechanically strong against delamination due to their intrinsic layered structures. As a result, the delamination issue has become one of the major design challenges of REBCO magnet coils. As a part of the development of the 40 T all-superconducting magnet at the National High Magnetic Field Laboratory, USA, large-scale coils wound by two-in-hand REBCO conductor with turn-to-turn insulation was designed and tested at 4.2 K in an 11.4 T background magnetic field. We found REBCO degradations within the windings and at the crossover joints during the tests. The postmortem inspection found that the degradation was caused by delamination. The delamination appears on the surface of the conductor as bubbles which were subsequently studied by microscopy. Additionally, a similar bubble was found on a short sample by torque magnetometry. This supports the inference that the delamination bubbles found in coils are due to electromagnetic stress. In this paper, we present these findings. The implication of these findings for future magnet designs and the method of mitigation will be discussed.

Interaction with intelligent systems is expanding beyond text-centric chatbots and coding agents. Speech-native assistants, visual generation and editing, world-model environments, and robot action loops require models that emit text, audio, images, video, and actions. These models differ in execution pattern: multi-stage autoregressive omni and TTS pipelines, iterative diffusion or flow-matching generators, and longer-lived world-model or robot loops that carry state across steps. As a result, serving is no longer a single text decode loop, but a heterogeneous multi-stage workflow with cross-stage transfer, streaming, and session-shaped interaction. Existing inference stacks are typically optimized for one architecture family. LLM servers deepen autoregressive scheduling and KV management, while diffusion stacks deepen denoising and parallel generation. Neither provides a shared control plane for pipelines that emit speech, pixels, or actions through separate generators, so production deployments often fall back to ad-hoc composition across disjoint runtimes. We present vLLM-Omni, a unified serving runtime for omni-modality generation. vLLM-Omni organizes each workload as a multi-stage pipeline under a single orchestrator that admits requests, advances them across stages, and demultiplexes streaming outputs. Specialized engines and stage replicas provide compute; a connector carries heavy payloads on the data plane; and session-oriented control supports long-lived duplex, world-model, and robot workloads. This report covers the architecture (stage-level KV paths, replica pools, multi-hardware platforms, and efficiency stack) and OpenAI-compatible and OpenPI APIs for omni, TTS, image/video, world-model, robot, and duplex workloads. We evaluate on the multimodal nightly CI on H100 (TTS and MiniCPM-o on H200), focused on Qwen3-Omni.

Naturalistic movie-fMRI provides a shared, temporally structured probe of brain dynamics, yet predictive models commonly rely on whole-run functional connectivity (FC) or temporally generic representations that are not aligned with narrative events. We introduce MovieSTAGE (Scene, Transition, and Global Encoding), a multiscale framework that combines hypergraph-structured FC-profile organization within scenes, unsigned FC-profile differences across adjacent scenes, and whole-movie FC. We evaluated 260 participants from the CMI-HBN Despicable Me cohort on case-control, ADHD-subtype, and three-class classification using 10 repetitions of stratified five-fold cross-validation, complete out-of-fold (OOF) predictions, and paired subject-cluster bootstrap and permutation tests. MovieSTAGE achieved AUROCs of 0.69, 0.73, and 0.75 and balanced accuracies of 67.6%, 69.8%, and 58.3%, respectively, yielding the highest mean point estimates among the evaluated methods. On the three-class task, the full model outperformed all two-branch variants, the HGNN scene encoder outperformed MLP, GAT, and BNT alternatives under matched settings, and the human-annotated partition outperformed duration-matched random and fixed-count GSBS controls. These controlled results support incremental predictive value from event-aligned scene and transition representations when combined with whole-movie FC in this cohort. Post-hoc model-derived analyses generated network-level hypotheses involving frontoparietal and default-mode systems.

Benchmarks for measuring the quality of action-conditioned world models are still evolving and shifting away from visual similarity-based metrics to action-semantic and physically-grounded metrics. However, for domain and task-agnostic action-conditioned world model training, existing benchmarks provide a limited signal. By training and evaluating diffusion world models on CounterStrike gameplay data, we confirm that qualitative playability does not correspond with metrics such as FVD, LPIPS, and JEDi. We term this the Virtual2Real gap. We posit that, in lieu of reliable benchmarks, curating raw gameplay data and measuring a variety of diagnostic properties provides a more robust signal to bridge the gap, before the training even begins. We present several curation strategies and a general-purpose kit for physical AI data curation called Kuration SDK, which is being open-sourced with this paper. The SDK was instrumental in uncovering the root cause of the virtual2real gap in a specific case: why two world models trained on identical gameplay map, action and state distribution, behaved very differently when played in spite of having very similar LPIPS and FVD scores. Thus, Kuration SDK has the potential to uncover the root causes of Virtual2Real gap in specific datasets and accelerate development of sample-efficient training datasets.

Facial movements convey subtle and important information that is critical for human social communication. Optical methods for face capture are difficult or impossible to use when the face is occluded by head-mounted devices (HMDs), such as VR headsets. Even with a clear line of sight, such methods raise privacy concerns and require head-mounted capture rigs that offset cameras and lighting from the face. We show that high-density surface electromyography (HD-sEMG) provides a viable non-optical alternative that addresses these challenges. We measured 64 EMG channels, using two textile EMG grids, with 32 from the forehead (typically occluded by an HMD) and 32 from the side of the face. EMG data were digitized at 2048 Hz and filtered. Facial movements were simultaneously recorded and used to estimate 478 3D facial landmarks using MediaPipe's Face Landmarker. A major challenge in such multimodal recordings is synchronizing EMG and video data, which have different sampling frequencies and independent clocks. We developed a novel synchronization method using analog audio bursts that is capable of sub-millisecond synchronization. We also developed a staged fitting method that fits a recent high-resolution parametric head model (GNM), with 253 identity blendshapes and 383 expression blendshapes, to the MediaPipe landmarks as participants performed different facial expressions. We trained a deep neural network comprising per-grid spatial encoders followed by a dilated temporal convolutional network (TCN) to predict blendshape parameters from HD-sEMG signals at 100 Hz. Once trained, the network can predict expression blendshapes solely from HD-sEMG recordings. The output can be rendered using standard real-time blendshape animation methods. We demonstrate the methods using recordings from 25 participants, and direct expression transfer to a variety of human faces and non-human characters.

We study a semidefinite programming (SDP) relaxation for community recovery when the number of communities grows logarithmically. In the balanced stochastic block model with $n=km$ vertices, we consider the regime $k/\log m\to\gamma>0$, with edge probabilities $\alpha\log m/m$ within communities and $\beta\log m/m$ across them, for fixed $\alpha>\beta>0$. We derive the sharp asymptotic tightness boundary away from critical cases. When rare vertices cause tightness to fail while the bulk remains spectrally stable, the normalized matrix error of every near-optimal solution still vanishes. We prove matching high-probability exponents for this error and the normalized optimal objective gain, governed by the same local correction that determines tightness. Throughout this spectrally stable region, a single SDP solve followed by explicit rounding and refinement achieves exact community recovery above the information-theoretic threshold. This guarantee holds even when the planted community matrix is not an optimal solution to the SDP.

Safe navigation in dynamic environments requires robots to plan under obstacle predictions whose errors are uncertain, non-stationary, and can induce rare but safety-critical failures. Existing control-barrier-function safety filters can reject immediately unsafe controls, but they provide little guidance on when the current finite-horizon planning mode itself is becoming unsafe as prediction uncertainty evolves. We propose Conformal Event-Triggered Risk-Certified Replanning (CERT-Replan), a framework that uses calibrated barrier risk as an early-warning signal for replanning. CERT-Replan calibrates horizon-indexed obstacle-prediction residuals online and uses the resulting uncertainty radii to evaluate dynamic-obstacle safety margins. A one-step safety filter protects the next applied control, while a horizon-level risk monitor evaluates the upper-tail CVaR of predicted barrier-violation losses along the current MPC rollout. When this risk exceeds an allocated budget, CERT-Replan rejects the current planning mode and selects a lower-risk alternative, such as a different speed profile, corridor, or homotopy class, rather than repeatedly correcting the same nominal plan. In a non-stationary benchmark, CERT-Replan achieves an \(83.3\%\) collision reduction relative to the safety-filter-only baseline \textcolor{black}{and a \(77.8\%\) reduction relative to simple replanning triggers}, while reducing average safety-filter intervention by \(32.4\%\). \textcolor{black}{With Trajectron++, CERT-Replan achieves \(96\%\) collision-free operation. Hardware experiments and onboard runtime profiling demonstrate computational feasibility.}

We propose an energy-stable arbitrary Lagrangian-Eulerian (ALE) finite element formulation for incompressible Navier-Stokes flows with surface-tension-driven free boundaries. The key ingredient is a multiplier-free compensated tangential velocity formulation, which redistributes boundary nodes via the discrete tangential curvature residual. The relaxation parameter governing the artificial tangential velocity is scaled according to the viscous-capillary balance, yielding the natural choice $\alpha= \gamma_0/ \mu $, where $\gamma_0$ is the surface tension coefficient and $\mu$ is the dynamic viscosity. We prove that the fully discrete scheme is well-posed, energy-dissipative, and temporally consistent with its semi-discrete counterpart. Numerical results confirm the robustness of the proposed method across a range of $\mu$ and $\gamma_0$ values. Furthermore, the method exhibits superior mesh quality preservation compared with the BGN method, particularly in the small-time-step regime.

In this paper, we investigate graphs with the property that all of their powers are well-covered. We obtain complete classifications for several graph classes, including chordal graphs, cochordal graphs, and very well-covered graphs.

We derive error bounds from empirical squared residuals for two non-monotone, mesh-free approximations of Hamilton–Jacobi–Bellman equations on unbounded spatial domains: collocation with Wendland kernels under a native space norm constraint, and physics-informed neural networks with smooth activations under a Sobolev-norm constraint. The main step is to recover the pointwise residual control needed for viscosity-solution error estimates from the empirical loss, while quantifying the discretization or sampling error. For the kernel method, we prove uniform convergence on compact sets under classical and native space regularity and derive an a posteriori quantitative error bound for the unique bounded continuous viscosity solution. For the neural-network method, we prove uniform convergence on compact sets in probability and give a quantitative high-probability error bound under classical Sobolev regularity. The bounds are governed by the fill distance for kernels and by the network and sample sizes for neural networks. The proofs combine empirical-to-population estimates, an interpolation inequality that turns an $L^2$ residual into a sup norm bound, and a controlled diffusion estimate for the error caused by truncating the domain. The regularity assumptions used to obtain convergence from approximation properties are additional to viscosity wellposedness. Numerical experiments in one and two space dimensions illustrate the methods and the estimates.

Let $k$ be algebraically closed of characteristic $p$. Reichstein and Vistoli showed that every $\Z/p^n$-torsor becomes at most one-dimensional over a field extension of degree prime to $p$, and Ledet conjectured $\ed_k(\Z/p^n)=n$. Using the finite-degree profile $\edd d_k(\tau)$ and its jump degrees introduced in \cite{PA}, we study the generic $\Z/p^n$-torsor $\tgen$, whose profile records how many Artin–Schreier–Witt layers an extension of degree $\le d$ can absorb. An Abel–Jacobi rigidity argument, in which the purely transcendental total space of $\tgen$ forces divisor classes on twisted curves to be constant, shows that a $G$-stable linear system on a faithful $\Z/p^n$-curve has degree $\ge p^{n-1}$. Hence $\edd d_k(\tgen)\ge2$ for $d<p^{n-1}$ and $d_1(\tgen)=p^{n-1}$ for all $p$ and $n\ge2$; in particular the truncation tower is optimal in degree $p^{n-2}$. We prove a quantitative Reichstein–Vistoli theorem, $d_1^{(p')}(\tgen)\le l_n(p)=1+(p-1)\sum_{j=1}^{n-1}p^{2j-1}$, and show that it is attained: $d_1^{(p')}(\tgen)=l_n(p)$ for all $p$ and $n$. We determine the profile at $(p,n)=(2,2)$ and every slot but the first at $(2,3)$, where the remaining slot is $\ed_k(\Z/8)\in\{2,3\}$, that is, Ledet's conjecture at level $3$. We show that the subgroup formula $\edd{p}_k(\tau_n)=n-1$ is equivalent to Ledet's conjecture at level $n-1$ together with a statement about extensions of degree $\le p$ disjoint from $L$, so that the profile relocates, but does not decide, Ledet's conjecture.

In recent years, Graph Neural Networks (GNNs) and architecture search frameworks have gained extensive application in non-Euclidean data processing, attributable to their superior capacity in managing unstructured data. Nevertheless, traditional approaches typically apply uniform convolution operations to all nodes, regardless of their varying structural and feature characteristics, which can undermine model performance and result in over-smoothing issues as the number of layers increases. To overcome this limitation, in this work, we propose a Node-Level Graph Neural Architecture Search (N-GNAS) algorithm. It can automatically choose an appropriate network architecture for each subset of nodes when updating node features. N-GNAS also introduces a contrastive learning loss to separate sample features from different categories and vice versa. In experiments conducted on eight datasets for node and graph classification, our methodology outperforms current leading GNAS techniques and traditional human-designed GNNs. For example, it achieves an accuracy rate of 78.26% on the CiteSeer dataset.

AI evaluation shapes the decisions of model providers, users, funders, and regulators. We argue that designing valid benchmarks requires contextualizing design choices in the dynamics of this ecosystem of actors. We develop a simulation architecture that combines rule-based market dynamics with LLM-driven strategic actors, building on advances in Generative Agent-Based Modeling (GABM). We model benchmarks, consumer needs, and provider capabilities as vectors over a six-dimensional capability space (reasoning, coding, knowledge, safety, communication, agentic), with structural information partitions across actors. As a case study, we apply this stylized simulation to explore benchmark holdout design. We find that moving from public benchmarks to private holdout benchmarks shrinks the gap between benchmark scores and user satisfaction on most benchmarks but widens it on a few, depending on where holdout weights shift scoring credit. We stress-test our findings at both the instrument and case-study level, drawing on the V&V framework of Sargent (2013) and GABM-specific evidence criteria. Beyond holdout design, our simulation is a hypothesis-generating sandbox for studying how evaluator and policy choices, in turn, reshape the ecosystem.