Machine Learning (Statistics)
FOCUS: Fixed-Confidence Online Causal Learning Using Sequential Adaptive Interventions
Haijie Xu and Chen Zhang
We study fully online fixed-confidence causal discovery without any historical observational data. Starting from zero samples, the learner sequentially selects interventions to recover both the causal DAG and its edge weights under a linear-Gaussian structural equation model. We establish an instance-dependent lower bound for any $(\epsilon,\delta)$-correct
algorithm and propose FOCUS, which adaptively allocates interventions through an online max–min game. A key contribution is a computable concentration inequality for the accumulated KL divergence involving causal parameters shared across interventions. We prove that FOCUS is $(\epsilon,\delta)$-correct and that its expected stopping time matches the lower bound in its $\Theta(\log(1/\delta))$ dependence up to an instance-dependent constant. Experiments demonstrate improved structure and edge-weight recovery and confirm the predicted stopping-time trend. Our codes are available on https://anonymous.4open.science/r/FOCUS_code-76E5
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High Energy Astrophysical Phenomena
Spin wandering of an accreting neutron star near torque balance: implications for gravitational wave searches
Andrew Melatos
Torque balance between gravitational radiation reaction and magnetocentrifugal
accretion is one reason why accreting
neutron stars rotate slower than centrifugal break-up. Random processes in the
accretion disk, such as Rayleigh-Taylor instabilities and flicker noise, drive the
spin frequency $f_\ast$ and gravitational wave frequency $f_{\rm gw}\propto f_\ast$ to wander stochastically around their torque balance values. Here it is shown theoretically, in terms of an idealized Ornstein-Uhlenbeck model, that the standard deviation of $f_{\rm gw}$ is given by $\sigma_{f_{\rm gw}}(h_0) \propto f_{\rm gw} h_0 D \beta T^{1/2}$, or equivalently $\sigma_{f_{\rm gw}}(F_{\rm X}) \propto f_{\rm gw}^{1/2} F_{\rm X}^{1/2} D \beta T^{1/2}$, where $h_0$ is the characteristic wave strain, $F_{\rm X}$ is the X-ray flux, $D$ is the source distance, and $\beta$ and $T$ are the fractional amplitude and autocorrelation time-scale of the
stochastic torque. One can use $\sigma_{f_{\rm gw}}(h_0)$ and $\sigma_{f_{\rm gw}}(F_{\rm X})$ to check the physical consistency of a detection candidate in a gravitational wave search by comparing with $\sigma_{f_{\rm gw}}$ observed.
Spin wandering impacts search design, because it sets the maximum time interval $\max(T_{\rm coh})$, during which the signal may be treated as coherent. The Ornstein-Uhlenbeck calculation predicts $10^{-1} \lesssim \max(T_{\rm coh}) / (1\, {\rm day}) \lesssim 10^3$, with $3\times 10^{-2} \lesssim \beta T^{1/2} / (1 \, {\rm s^{1/2}} ) \lesssim 4$, for Rayleigh-Taylor instabilities and flicker noise. The predicted $\max(T_{\rm coh})$ is shorter typically than the year-long observation runs of audio-band interferometers operating today, emphasizing the utility of semi-coherent search
algorithms, which divide the data into multiple coherent segments of duration $\max(T_{\rm coh})$.
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Computer Vision
PQR3D: Progressive Query Refinement over Reference-Conditioned Temporal Windows for Multi-View 3D Object Detection
Hui Ye, Yudong Liu, Yiran Chen et al. (+2 more)
Temporal context is essential for camera-only multi-view 3D object detection. Existing streaming detectors maintain and propagate query states from one frame to the next, requiring sequence-aware training and chronological inference. We propose PQR3D, which performs progressive query refinement within referenceconditioned temporal windows. This design enables random frame sampling and independent inference without persistent query
memory. Within each window, PQR3D progressively transfers motion-aligned high-confidence queries from earlier timestamps toward the target frame. We further introduce masked selfattention to regulate interactions among regular, propagated, and denoising queries while keeping denoising supervision isolated from detection queries. In addition, a stage-decoupled anchor
embedding injects position before self-
attention and size, orientation, and velocity afterward, reducing interference from temporally inconsistent attributes. With a ViT-L backbone, PQR3D sets a new state of the art on the nuScenes test set, achieving 71.6 NDS and 64.9 mAP. Source code is available at https://github.com/huiyegit/PQR3D
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All authors Hui Ye, Yudong Liu, Yiran Chen, Rajshekhar Sunderraman, Shihao Ji
Computer Vision
PruneForget: Joint Unlearning and Pruning of Vision Models
Yu-Shan Tai, Amber Yijia Zheng and Raymond A. Yeh
Machine unlearning and model
pruning are increasingly coupled in the real world. Models must support unlearning requests, e.g., for safety concerns, while also meeting requirements in latency and
memory budget. Until recently, existing works have studied each aspect as an independent problem, e.g., running unlearning and
pruning sequentially. In this work, we show that unlearning and
pruning are naturally aligned and should be solved jointly to be made aware of each other. Intuitively, parameters that encode information of the unlearned samples are natural
pruning targets, as unlearning and
pruning both call for the "deletion" of such parameters. We propose PruneForget, a method that uses the unlearn set as a guide for
pruning, so that unlearning and
pruning mutually benefit each other. Extensive experiments on image classifiers and generative models show that PruneForget removes the influence of the unlearned samples while producing a more compact model with reduced inference cost. It achieves a negligible performance gap relative to an oracle that retrains from scratch for unlearning and then prunes.
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Combinatorics
Weak $k$-metric dimension of Hamming graphs: rectangular products and near-maximum parameters
Aryan Kumar
We determine weak $k$-metric dimensions for several families of Hamming graphs. For $n\ge3$, $m>n$, and $3\le k\le2n$, a cyclic construction proves
Conjecture 6.1 of Fernández, Klavžar, Kuziak, Muñoz-Márquez and Yero (2026) on $K_n\square K_m$. For these rectangular products, we also prove that $\operatorname{wdim}_2(K_n\square K_m)=m$ exactly when $m\ge2n-2$. For hypercubes $Q_d$ with $d\ge2$, we show that consecutive parameters $2s-1$ and $2s$ have identical weak resolving sets. Near the maximum parameter, a reduction to restricted-distance binary codes determines $\operatorname{wdim}_{2^d-t}(Q_d)$ for every feasible deficit $0\le t\le15$. For $L\ge1$ and $t\in\{2L,2L+1\}$, we prove the stabilization formula $\operatorname{wdim}_{2^d-t}(Q_d)=2^d-L$ for $d\ge2^L+1$, and show that this threshold is sharp. For each fixed $q\ge3$ and deficit $t$, we also determine $\operatorname{wdim}_{2q^{d-1}-t}(K_q^{\square d})$ in all sufficiently large dimensions, with an explicit sufficient condition.
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Computation and Language
Typed Decision Models: An Early Evidence Audit and Evaluation Checklist
Lijuan Tang and Yuemeng Zheng
Typed decision models (TDMs) return probability distributions over caller-defined options without generating text. TypeSafe released Jev, a commercial typed decision model, on 15 September 2026, and a small body of evaluation and replication work appeared within days. We review 28 papers posted between 19 and 24 September and relate their findings to earlier work on label-probability classification, constrained decoding, reranking, calibration, and model cascades. In this early literature, the typed readout itself has not shown an independent accuracy advantage over comparable label-probability readouts. Jev's clearest gains are in latency and cost, while accuracy gaps remain on harder tasks. In practical deployments, confidence is often used to decide when to defer to a stronger model or a human. We use recurring weaknesses in these studies to derive a 14-item evaluation checklist for future TDM work. Because the evidence covers only the first nine days after the release of one hosted model, the review should be read as an early evidence map rather than a settled assessment of the model class.
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Astrophysics of Galaxies
H-alpha Star Formation Rates of the SHIELD Dwarf Galaxies
Madeline Shepley, David G. Gormanous, John J. Salzer et al. (+9 more)
The Survey of HI in Extremely Low-mass
Dwarfs (SHIELD)
galaxy sample is an HI-selected catalog of
galaxies that occupy the extreme low-mass end of the HI mass function. Our team is carrying out a comprehensive multi-wavelength observational program targeting these gas-rich,
star-forming
dwarf galaxies. The current paper presents H-alpha narrowband observations of the full SHIELD sample. We detect 55 of the 82
galaxies (67%) with nebular H-alpha emission, and infer sensitive upper limits to the H-alpha fluxes for the 27 non-detections. We derive H-alpha luminosities and
star formation rates (SFRs), or upper limits, for all 82 SHIELD
galaxies. We also present, for the first time, deep broadband and continuum-subtracted H-alpha images plus a summary of the properties for the entire sample. Our analysis of the H-alpha data re-affirms previous results which show that at low levels of
star formation (log(SFR_{H-alpha}) < -2.5), H-alpha becomes an increasingly poor tracer of the recent average SFR as measured by far-UV (FUV) luminosities. However, we show that this effect is not strictly correlated with the mass of the
galaxy. Some very low-mass SHIELD
galaxies with higher H-alpha-based SFRs show good agreement with SFR_{FUV}. The SHIELD
galaxies show no correlation between H-alpha SFR and gas mass fraction, but reveal a modest correlation between H-alpha specific SFR and gas mass fraction. Overall, the
star formation efficiency exhibited by the SHIELD
dwarfs is rather low, despite the gas-rich nature of the sample (68% have M_{gas} > M_{
stellar}).
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All authors Madeline Shepley, David G. Gormanous, John J. Salzer, Nathalie Haurberg, Steven Janowiecki, John M. Cannon, Elizabeth A. K. Adams, Martha P. Haynes, Alec S. Hirschauer, Kristen B. W. McQuinn, Katherine L. Rhode, Evan D. Skillman
Robotics
FutureRay: Control-Aligned Future Range for Agile Quadruped Navigation
Tianhao Zang, Shanze Wang, Ziqian Wang et al. (+4 more)
Moving obstacles can block a previously clear route while a quadruped
robot executes a motion command. We investigate whether predicting changing clearance improves
navigation when motion selection accounts for the
robot footprint and the time needed to react and brake. We present FutureRay, which predicts ranges across viewing directions and future times, together with encounter risk, from depth-derived range history and observable
robot motion. Training emphasizes near-term clearance and penalizes errors that overstate available space. A local planner queries the same forecast for candidate headings and combines it with current observations to check clearance around the
robot footprint. Model-based reaction–braking limits guide speed selection, and the resulting velocity commands are passed to a fixed locomotion policy. In paired evaluations on 60 static and dynamic simulation scenes, FutureRay achieves 93.3% completion, compared with 75.0% for current-range persistence and 80.0% for Cartesian Kalman rollout, with perception, planning, and locomotion held fixed. FutureRay also records fewer collisions than both baselines. Qualitative trials on a physical quadruped show avoidance initiated while an obstacle is approaching the route, followed by renewed goal progress. These results show that joint range and encounter-risk prediction can improve obstacle avoidance without retraining the locomotion policy.
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All authors Tianhao Zang, Shanze Wang, Ziqian Wang, Liyou Luo, Zihan Liu, Xingjian Xie, Wei Zhang
Computer Vision
CausalDriveBench: Evaluating Causal Reasoning in Vision-Language-Action Models for Autonomous Driving
Narendiran Chembu, Navvrat Rao, Shreedhar Shreeshail Kodate et al. (+10 more)
Vision-
Language-Action (VLA) models for autonomous driving produce natural-
language reasoning alongside predicted trajectories, but whether this
reasoning reflects the causal structure of the scene remains untested. We introduce CausalDriveBench, an evaluation framework grounded in Pearl's Causal Hierarchy (PCH) that tests causal
reasoning in driving-specific VLAs through structured visual question answering (QA) and alternative-trajectory prediction. To this end, we construct causal scene graphs over nuScenes that distinguish causally active, dormant, and distractor entities, separating perceptual salience from causal relevance. The
benchmark spans all four rungs of PCH (association, intervention, and counterfactual along with causal discovery) for QA generation. For the higher rungs, we additionally provide reference trajectories under specified scene modifications, enabling action-level verification that complements
reasoning-level evaluation. In total, the
benchmark contains 7,285 verified causal QA pairs and 1,000 counterfactual trajectories derived from nuScenes. We evaluate 10 driving-specific VLAs and 3 general-purpose VLMs, and report three findings. First, the best model reaches only 70.6% QA accuracy, and 4 of 13 models score below random chance. Second, comparing each driving VLA to the general-purpose VLM that shares its
language backbone, the cost of driving fine-tuning ranges from 2 to 34 percentage points on causal QA, with post-training design explaining the spread. Third, causal QA and trajectory accuracy are statistically uncorrelated across models: under counterfactual
prompts, predicted trajectories either over-react or collapse onto the observed-scene baseline. Taken together, these results show that neither fluent rationales nor accurate observed-scene trajectories constitute evidence of causal understanding.
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All authors Narendiran Chembu, Navvrat Rao, Shreedhar Shreeshail Kodate, Gayatri Srujana Banda, Arko Sarkar, Abhinav Khanna, Rajarshee Das, Umesh Kanala, Siddarth Khandelwal, Kumar Aman, Aish Dubey, Kaustubh Beedkar, Arjun Jain
Robotics
AquaBEV-Nav: Learned BEV Occupancy for Underwater Navigation and Exploration
Trung Tien Dong, Zhenqi Wu, Sahasra Kondapalli et al. (+3 more)
Safe
underwater exploration requires a
robot to understand where surrounding structures are located and which regions are available for motion. Existing
vision-based
underwater exploration systems commonly obtain this information indirectly by estimating
monocular depth, unprojecting the geometry into 3D space, and accumulating it into a 2D bird's-eye-view occupancy map. This reliance on intermediate depth estimation is particularly problematic
underwater, where scattering and wavelength-dependent attenuation degrade visual cues and limit the reliability of
monocular depth estimates. We introduce AquaBEV-Nav, an
underwater exploration framework that bypasses explicit
monocular depth estimation through direct bird's-eye-view occupancy prediction. Built upon the CORAL hierarchical exploration framework, AquaBEV-Nav replaces its depth-based perception front end with AquaBEV. Given a single RGB frame, AquaBEV maps visual features into a learned polar representation, performs causal
reasoning along the range dimension, and reconstructs local Cartesian occupancy without relying on intermediate depth prediction. The resulting occupancy map is accumulated into CORAL's persistent spatial
memory, providing spatial context for VLM-based high-level planning and collision constraints for dynamics-aware local trajectory generation. Across ten simulated reef environments and six occupancy backbones evaluated under a single protocol, AquaBEV-Nav reaches 37.48 structure IoU and 53.2 target IoU, 88.95% closed-loop coverage with zero collisions.
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All authors Trung Tien Dong, Zhenqi Wu, Sahasra Kondapalli, Jiayi Wu, Yi Sheng, Xiaomin Lin
Robotics
RecastVLA: From Past Interaction to Future Control with Adaptive Policy States
Wenbo Li, Jun Yang, Yiteng Chen et al. (+2 more)
Sequential manipulation requires a
robot to track what has already happened, even when the current scene no longer reveals it. Policies with explicit history representations make past interactions available as context for current decisions. We ask how action generation itself can form a persistent state for subsequent control. Building on action-side test-time training, RecastVLA maintains an adaptive policy state within a flow-matching
vision-
language-action policy. The state is represented by shared fast weights and remains fixed throughout action generation. Depth-specific interfaces read the same state, while features across depths and flow evaluations jointly define one update for the next policy call. Subsequent action losses train the initialization, interfaces, and update rule by differentiating through earlier state transitions. At deployment, updates use the policy's own action-generation features without expert action labels. Across LIBERO, RoboTwin, RoboDojo, and twelve real-
robot tasks, RecastVLA improves mean success over a matched policy trained without test-time training, including 10.68 percentage points on RoboTwin Clean-to-Clean. In controlled RoboTwin comparisons, retaining state improves success, and the shared design exceeds independently trained layer-local TTT by 2.58 points.
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All authors Wenbo Li, Jun Yang, Yiteng Chen, Wei Zhang, Qingyao Wu
Robotics
GAUGE: Planner-Conditioned Active Calibration of Opaque Quadruped Velocity Interfaces
Tianhao Zang, Zihan Liu, Shanze Wang et al. (+4 more)
In this paper, we present a Goal-Aware Uncertainty-Guided Exploration (GAUGE) framework for planner-conditioned active calibration of opaque quadruped velocity interfaces. Commercial quadrupeds commonly expose planar-velocity commands, but the underlying locomotion controller remains inaccessible and can produce systematic discrepancies between commanded and realized motion. A
navigation planner typically uses a structured subset of the command envelope. GAUGE maintains a
Bayesian command-to-motion model and selects authorized trials according to their expected reduction of posterior epistemic uncertainty under the planner-induced command distribution. The resulting posterior supports validation-based stopping, bounded inverse compensation, and task-relevant recalibration after detected interface shifts. In three controlled response families, GAUGE reaches the joint criterion for task-facing accuracy and uncertainty with fewer trials than passive, D-optimal, and task-agnostic alternatives. Across six held-out Isaac Sim
navigation maps, it meets the declared noninferiority margins against dense calibration. Code is available at https://github.com/EurekaZang/CalibAgent.
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All authors Tianhao Zang, Zihan Liu, Shanze Wang, Liyou Luo, Xingjian Xie, Chengtai Li, Wei Zhang
Distributed Computing
ThreadShift: Transparent Thread-Level Offloading on Transient Cloud Resources Using MPKs
Antoine Murat, Clément Burgelin and Rachid Guerraoui
Transient cloud resources offer significant cost savings, but their unpredictability makes them hard to use for applications that cannot be safely restarted after reclamation. Existing approaches require application changes or rely on coarse-grained checkpointing, whose cost limits its benefits. We present ThreadShift, a system that transparently offloads compute-intensive threads of unmodified Linux applications to cheap transient resources while preserving correctness under reclamation. By operating at thread granularity, ThreadShift enables fast, fine-grained checkpointing and offloads only the threads that benefit from transient execution. The main challenge is to checkpoint individual threads despite cross-thread dependencies. ThreadShift does so by efficiently tracking
memory dependencies, identifying per-thread
memory writes, and maintaining coherence across machines. Three novel uses of
Memory Protection Keys (MPKs) make these mechanisms efficient, enabling fast incremental checkpoints without pausing the entire application. We implement ThreadShift on x86-64 Linux and evaluate it on workloads including machine-learning inference, cryptographic tasks, and in-
memory data processing. ThreadShift offloads threads in as little as 164 us, performs checkpointing up to three orders of magnitude faster than CRIU, and reduces deployment cost by up to 56% on commodity clouds.
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Group Theory
The finite basis problem for additively idempotent semirings of order four, IV
Miaomiao Ren, Mengya Yue, Mengyu Yuan et al. (+3 more)
This paper is the fourth in a series devoted to the finite basis problem for $4$-element additively idempotent semirings. These
algebras are divided into five types according to their additive reducts; we study the largest of these types, namely those whose additive reducts are chains. Up to isomorphism, there are $386$ such
algebras, denoted by $S_{(4, k)}$, $481 \leq k \leq 866$. We show that all but three of them, namely $S_{(4,545)}$, $S_{(4,634)}$, and $S_{(4,710)}$, are finitely based. This completes the classification, with respect to the finite basis property, of all $4$-element additively idempotent semirings with chain additive reducts.
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All authors Miaomiao Ren, Mengya Yue, Mengyu Yuan, Simin Lyu, Chenyu Yang, Ting Yu
Combinatorics
Anti-Ramsey Number of Intersecting Odd Cycles
Haojie Zheng
For a graph $H$, the anti-Ramsey number $\operatorname{ar}(n,H)$ is the maximum number of colors in an edge-coloring of $K_n$ containing no rainbow copy of $H$, where a copy is rainbow if its edges have pairwise distinct colors. Let $s,t$ be nonnegative integers with $s+t\ge2$, and let $H_{s,t}$ be a graph consisting of $s$ triangles and $t$ odd cycles of fixed lengths at least $5$, all sharing exactly one common vertex and otherwise pairwise vertex-disjoint. Liu et al. (2024) determined $\operatorname{ar}(n,H_{s,0})$ for $s\ge3$ and $n\ge50s^2$. In this paper, we determine the exact value of $\operatorname{ar}(n,H_{s,t})$ for every fixed $H_{s,t}$ with $t\ge1$ and all sufficiently large $n$.
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Computational Engineering
CompFlowLab: A Python code to develop and prototype new data-driven models for challenging compressible flow problems with shocks and chemical reactions
Ali Mohaghegh and Cheng Huang
CompFlowLab is an open-source Python environment that is capable of modeling different classes of compressible flow problems (including shocks, flames, and detonation waves) using a one-dimensional compressible Navier-Stokes solver with multi-species transport and chemical-reaction models. It is designed specifically for the data-driven modeling community as a lightweight, accessible prototyping platform to test, develop, and evaluate new modeling methods on numerically and physically challenging compressible flow problems, especially those featuring shocks and chemical reactions. Specifically, CompFlowLab aims at (1) providing computationally efficient calculations on advection-dominanted problems that are well-recognized to be difficult for conventional data-driven modeling techniques, such as shocks, flames, and detonation waves, and more importantly (2) enabling rapid testing and prototyping of new data-driven models. The code serves three primary purposes: (1) generating high-fidelity full order model data for training of data-driven modeling, (2) providing a modular platform for implementing and testing novel data-driven
algorithms (e.g., machine learning methods and reduced-order modeling techniques) on challenging physics, and (3) offering a standalone Computational Fluid Dynamics (CFD) solver with validated test cases that can also support numerical method development in the broader CFD community. By unifying these capabilities in a clean, extensible Python codebase, CompFlowLab lowers barriers to innovation at the intersection of model reduction and complex fluid dynamics.
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Machine Learning (Statistics)
A Unified Optimism-Agnostic Framework for Linear Bandits over Spherical Action Sets
Arda Güçlü, Subhonmesh Bose and John R. Birge
Linear bandits model sequential decision-making problems with noisy rewards that are linear in the decision variable, where an
agent must simultaneously learn about an unknown parameter that governs the mean rewards, while maximizing (expected) rewards over time. Two prominent algorithmic families–upper confidence bound (UCB) and Thompson sampling (TS)–achieve a balance of exploration (to estimate said parameter) and exploitation (utilization of knowledge about it) across time. The quality of estimation of that parameter depends on the
eigenvalues of a design
matrix. In this paper, we begin by showing that if the inference quality obtained from exploration, encoded in the minimum
eigenvalue of the design
matrix, grows $\gtrsim \sqrt{t}$ with time $t$, while actions remain sufficiently concentrated for exploitation, then an
algorithm produces optimal high-probability $\mathcal{O}(\sqrt{T}\log T)$-regret rate over a time-horizon $T$ for spherical action sets. This analysis is
algorithm-agnostic and follows an alternative route to the classical optimism-based elliptical-potential argument for regret analysis. Then, we illustrate that variants of UCB and TS satisfy the inference and concentration properties and in turn, enjoy optimal regret rate. In effect, our results provide a modular framework that can be used to analyze linear bandit
algorithms and explicitly connect quality of parameter estimation to optimal regret accumulation.
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Analysis of PDEs
On elastic scattering behavior of corner domains
Pu-Zhao Kow, Mikko Salo and Henrik Shahgholian
We investigate the scattering of elastic waves by anisotropic inhomogeneous media at a fixed wave number. We prove that, in two dimensions, every penetrable obstacle with piecewise $C^{1}$ boundary and corner singularities, and, in higher dimensions, every obstacle with edge singularities, scatters every incident wave satisfying suitable assumptions. This work extends our previous result [J. Math. Anal. Appl. 2026, doi:10.1016/j.jmaa.2026.130630] from scalar equations to systems of equations, a generalization that requires a more delicate blowup analysis and more involved computations. Roughly speaking, our results establish the principle that corners always scatter for general anisotropic media with variable coefficients.
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Fluid Dynamics
A deterministic Fokker–Planck/lattice-Boltzmann micro–macro solver for dilute Hookean polymer solutions
Xueqin Liu, Shi Shu, Yaolong Yu et al. (+3 more)
Deterministic micro–macro simulation of
polymer solutions requires the coupled
evolution and spatial transport of a configuration distribution, together with the conversion of its moments into macroscopic stress and feedback to the flow. We develop a Fokker–Planck/
lattice-Boltzmann solver for this coupling in two-dimensional dilute Hookean
polymer solutions. The solver represents the distribution on the unbounded configuration space by Hermite coefficient fields, advances local configuration dynamics and physical-space transport in separate steps, and recovers Kramers stress from the second moment to achieve two-way coupling with a purified two-relaxation-time
lattice-Boltzmann flow solver. To assess whether this configuration description recovers the corresponding macroscopic response, we use the exact second-moment closure of the continuous Hookean model as a macroscopic reference for comparison with analytical and independently discretized macroscopic solutions. The calculations reproduce velocity overshoot and damped oscillations in start-up Poiseuille flow, with velocity profiles approaching the analytical start-up transient under grid refinement; in four-roll flow with spatially nonuniform extension and stress feedback, the maximum full-domain relative differences in velocity and
polymer stress are approximately $0.0309\%$ and $3.84\%$, respectively, over the tested Weissenberg numbers at corresponding sampling times. These comparisons support the solver's ability to recover the Hookean macroscopic response from configuration-distribution
evolution. Further calculations of wall-bounded recirculation and open cross-slot flow exhibit the corresponding conformation responses and symmetric and asymmetric flow states, extending this deterministic micro–macro method to viscoelastic flows under different boundary constraints.
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All authors Xueqin Liu, Shi Shu, Yaolong Yu, Yuan Yu, Hao Zhang, Yuting Zhou
Machine Learning
Playing to Par: Reinforcement Learning for Provably Optimal Quadrilateral Block Decompositions
Arjun Narayanan and Per-Olof Persson
A quadrilateral block decomposition of a planar domain is judged by whether it is complete, whether its elements are well shaped, and how many of its vertices are irregular. The last has a provable floor: the discrete Gauss-Bonnet identity enforces a lower bound on the total vertex irregularity of any all-quadrilateral mesh of a given domain purely based on its
topology and corner angles. We train a reinforcement learning
agent to build decompositions that reach this bound, which we call par. It acts directly on the mesh's half-edge data structure through local edits, with a policy network whose convolutions follow the mesh's own connectivity, so it applies unchanged to domains larger than any seen in training. The reward targets the floor directly, and it is sparse: random play reaches it on no domain with more than eight sides. We overcome this exploration barrier via behaviour cloning on optimal meshes that are trivial to construct, walked backward into demonstrations, before training it with PPO. On 96 held-out domains the
agent produces an all-quadrilateral mesh on every one, a usable one on 95.7 on average, and a provably optimal one on 90; Gmsh's strongest configuration at the same element count completes 51, is usable on 38 and optimal on none, and even at three to fourteen times the elements never produces a more regular mesh. On 64 domains twice the training size the
agent completes all, is usable on 62, and keeps a median excess over par below one against Gmsh's 39 at the same element count.
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Analysis of PDEs
Isoperimetric clusters with a liquid phase
Jake Wellington
A wet foam is a cluster of air chambers whose interfaces are coated by a single
liquid chamber of prescribed volume. In the corresponding isoperimetric problem the
liquid chamber may collapse onto films of zero thickness, so that minimizers need not exist. We identify the relaxed energy accounting for such collapsed films and prove that limits of minimizing sequences are its minimizers. The resulting compactness and energy representation
theorems lead to the regularity of these generalized minimizers, including an
equilibrium law for the pressures across collapsed films. Finally, as the
liquid volume vanishes, the minimal energies converge to those of the classical dry foam.
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Solar and Stellar Astrophysics
Self-constrained Magnetic Reconnection of a Solar Flare Co-spatial with a Non-ejected Filament
Ye Qiu, Changxue Chen, Anqin Chen et al. (+11 more)
For
flares associated with eruptive filaments, the filament normally rises above the post-
flare loops. Here, we report an unusual event in which the post-
flare loops instead overlie a filament that remains non-ejected throughout the
flare. This event was simultaneously captured by the Chinese H$\alpha$
Solar Explorer (CHASE), the
Solar Extreme-UltraViolet Imager (SUVI) onboard Fengyun-4C, the Hard X-ray Imager (HXI) onboard the Advanced Space-based
Solar Observatory (ASO-S) and the
Solar Dynamics Observatory (SDO). Extreme Ultraviolet (EUV) observations provided by FY4C/SUVI and SDO show that two hot loop systems form at the
flare onset. The western end of the northern loop system undergoes a southwestward drifting motion with gradually increasing shear, whereas the southern loop system progressively converges toward and eventually overlies the northern one. Meanwhile, three-dimensional
magnetic field extrapolations reveal an increase in both the twist of the filament-supporting
magnetic structure and its poloidal
magnetic field after the
flare. Taken together, these observations suggest that the
flare is driven by a self-constraining zipper-type
magnetic reconnection, in which highly sheared arcades reconnect to form a series of overlying
flare arcades and an underlying flux rope. This reconnection continuously strengthens the
magnetic confinement of the filament, preventing its outward eruption, while facilitating substantial
plasma drainage along the reconnected
magnetic field revealed by the CHASE H$\alpha$ spectroscopic observations.
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All authors Ye Qiu, Changxue Chen, Anqin Chen, Chuan Li, Yang Guo, Linggao Kong, Feng Lu, Xiaohu Zhang, Weiguo Zong, Jinsong Wang, Xinkai Li, Peng Wang, Kefei Song, Bo Chen
Machine Learning
Spectral Reversal: Counteracting Singular Value Bias for Graph Prompting
Hanxu Yang, Yuhuan Zhao, Xiaodong He et al. (+1 more)
Pre-training Graph Neural Networks (GNNs) via self-supervised learning has become a dominant paradigm, yet efficiently adapting frozen encoders remains a challenge. Graph prompting offers a parameter-efficient alternative to fine-tuning, but existing methods largely treat pre-trained models as opaque feature extractors, ignoring their internal spectral structure. In this work, we identify a systematic phenomenon in pre-trained GNNs, which we term spectral bias: optimization during pre-training disproportionately aligns representations with directions associated with large singular values, leaving low-energy directions under-explored. We show that these underutilized directions can encode complementary information that is beneficial for downstream adaptation, especially under distribution shift. To leverage this insight, we propose Spectral Reverse
Prompt (SRP), a prompting framework that rebalances the spectral contributions of frozen GNN encoders. SRP applies a learnable soft-thresholding mask in the spectral domain to down-weight dominant directions while amplifying weaker ones. In addition, SRP incorporates a null-space augmentation module that captures variation in directions with minimal activation under the frozen encoder. Extensive experiments across multiple
benchmarks demonstrate that SRP achieves state-of-the-art performance with minimal additional parameters, highlighting that reweighting spectral components is a principled and effective strategy for parameter-efficient graph adaptation.
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All authors Hanxu Yang, Yuhuan Zhao, Xiaodong He, Zhao Kang
Geophysics
Efficient One-Step Surface-Wave Tomography through Implicit Differentiation and Jacobian Factorization
Yiran Jiang, Ping Tong and Jianwei Ma
Surface-wave
tomography provides important constraints on the crust and upper mantle, but directly inverting millions of measurements for three-dimensional structure remains computationally demanding. We develop an efficient Gauss–Newton framework for one-step surface-wave
tomography that jointly inverts multiperiod interstation traveltimes for shear-wave velocity, accounting for both lateral wave propagation and depth sensitivity. Implicit differentiation of the converged discrete Eikonal equations provides individual traveltime sensitivity kernels, which are constructed efficiently by reusing the Eikonal dependency structure across receivers. A factorized Jacobian retains these kernels separately from shared model and dispersion mappings, reducing storage and repeated-product costs within each linearized solve. Synthetic experiments show that the framework recovers three-dimensional velocity anomalies with fewer model updates and lower model errors than the tested comparison workflows at similar data fits. Computational
benchmarks demonstrate substantial savings in operator storage and the cost of linearized model updates compared with using explicitly assembled Jacobians. We apply the framework to 6.34 million Rayleigh-wave phase traveltimes across the contiguous United States. The recovered model captures major crustal and uppermost mantle velocity variations, including the broad contrast between the tectonically active western United States and the continental interior, consistent with previous surface-wave studies. These results demonstrate a practical Gauss–Newton approach to imaging the crust and upper mantle using large surface-wave data sets.
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Machine Learning
REALM: Regime-Switching, Explainable, and Activation-Induced Linear Models
Xiaoran Cheng, Sen Na and Jia Li
Deep ReLU networks are piecewise-affine mappings that partition the input space into
cells, each characterized by a distinct activation pattern. This structure motivates fitting a local linear model within each
cell to preserve predictive accuracy while improving interpretability. The challenge is to identify regimes that are stable, data-adaptive, and easy to explain. We propose REALM, a mixture of linear models whose regimes are induced by neural activation patterns. Because the number of activation
cells in a deep neural network (DNN) can grow rapidly with depth, we first distill a deep teacher into a wide, shallow student network (WSSN), then binarize and cluster its hidden-layer activations to define the regimes and fit a linear model within each regime. Since the regimes are discovered from internal structure, the router does not carry the predictive burden. To make regime assignment interpretable, we train a multiclass logistic regression, the explanatory gate, to reproduce the regime assignments. The two-level structure is interpretable at both stages in terms of raw tabular or learned convolutional features: the gate identifies features that determine regime assignments, while the linear models identify features that drive predictions within each regime. We analyze an idealized setting that illustrates a trade-off between partition complexity and stability: as the number of regimes grows, finer partitions can improve approximation but may reduce regime-assignment stability. Experiments on tabular and image
datasets show that REALM achieves competitive predictive performance relative to other DNN-guided mixture surrogates and inherently interpretable models while producing stable regime-level explanations.
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Number Theory
Unit fractions with semiprime denominators: an elementary proof of Erdős Problem #306
Shisheng Li
We give an elementary proof that every positive rational number $a/b$ with $b$ squarefree is a finite sum of distinct unit fractions $1/n$, where each $n$ is a product of two distinct
primes (Erdős Problem #306). After a reduction to small targets, we take a single complete bipartite graph between the
primes in $(y^2,2y^2]$, together with $2$ and the
primes of $b$, and a tuned initial segment of the
primes in $(y^8,y^9]$, and show that some subgraph has reciprocal sum congruent to $a/b$ modulo $1$; the small total mass then forces equality. Writing the number of such subgraphs as a finite
Fourier sum, we sort the frequencies into three cases using a table indexed by the two sides of the graph. The small integer frequencies give a positive main term, and all other frequencies are negligible by a divisor-counting argument and a no-wrap-around form of the Chinese remainder
theorem. The only inputs about
primes are Chebyshev-type bounds. The circle-method framework comes from Tang's Lean development, which gave the first proof; our construction removes its anchor-synchronisation step. The proof has been formalised in Lean 4, apart from a cited inequality of Ramanujan. This work is a human-AI collaboration: AI tools contributed substantially to the construction, the experiments and the writing.
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High Energy Physics (Theory)
Hairy Taub-NUT solution in gauged supergravity
Masato Nozawa
We present and study a family of exact Taub-NUT-AdS solutions with scalar hair in four-dimensional ${\cal N}=2$ gauged supergravity. The solutions are supported solely by a nontrivial scalar field and its self-interaction potential, with all gauge fields switched off. We determine the conditions under which Killing horizons exist and demonstrate that the spacetime admits at most one Killing horizon, and whenever it exists it is necessarily nondegenerate. In particular, the NUT deformation can give rise to a horizon in a branch whose static limit is horizonless. We also establish that the solutions with nontrivial scalar hair admit no Killing spinors. As in ordinary Taub-NUT-AdS spacetime, the global structure is afflicted by closed timelike curves. We compute the conserved mass using the covariant phase space method and formulate a restricted first law with the NUT parameter held fixed. Finally, we study the Euclidean sector, including an exceptional family specific to Euclidean signature, and determine the regularity conditions for bolts and nuts.
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Number Theory
Factorizations in algebraic monogenic semidomains
Jiya Dani, Felix Gotti, Bryan Li et al. (+1 more)
We study the additive and multiplicative arithmetic of algebraic monogenic semidomains of the form $S_\alpha$. We first relate their structure to the conjugates of $\alpha$, characterize when $S_\alpha$ is a ring, and determine when its additive monoid is free. We then investigate units and prove a Dirichlet-type
theorem showing that $S_\alpha^\times$ is the product of a finite cyclic group of roots of unity and a finitely generated free abelian group; in particular, the unit group is free abelian when $\alpha$ is positive. We also give a criterion that produces non-atomic algebraic monogenic semidomains. Turning to finiteness properties, we prove that $\mathbb{Z}[\alpha]$ is a finite factorization domain for every algebraic number $\alpha$, establish criteria ensuring that $S_\alpha$ is a finite factorization semidomain, and construct infinitely many positive cubic generators yielding finite factorization semidomains that are not rings. Finally, we give a membership criterion for rational elements of $\mathbb{Z}[\beta]$ for arbitrary algebraic $\beta$, and prove that, for algebraic integers $\alpha$, unique factorization ascends from $\mathbb{Z}[\alpha]$ to $\mathbb{Z}[\alpha/n]$ for every $n\in\mathbb{N}$.
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All authors Jiya Dani, Felix Gotti, Bryan Li, Arav Paladiya
Astrophysics of Galaxies
Tracing Winds through the Fog: A Comprehensive Survey of LMC's Galactic Outflows with ULLYSES
Suraj Poudel, April Horton, Kathleen A. Barger et al. (+21 more)
We investigate nearside
stellar-driven
outflows from the Large Magellanic Cloud (LMC) using UV absorption-line spectroscopy of 170 OB
stars, complemented by HI 21-cm emission and H$_{\alpha}$ emission. Using Voigt-profile fitting and AOD analysis of SiII, OI, and SII transitions, we map the velocity-dependent structure of foreground gas. The SiII column densities for the Voigt-fitted components decline smoothly from the LMC disk and reach a minimum at $v_{\rm LMCSR} \approx -100$ to $-200~{km~s^{-1}}$, marking the transition from a denser, slower wind to more diffuse high-velocity material. Comparisons with local
star-formation rate surface densities reveal a modest positive correlation for the slower wind component, linking it to recent massive-
stellar feedback. Photoionization modeling of 13 absorbers in the $+100\lesssim v_{\rm LSR} \lesssim +150~{km~s^{-1}}$ range reveals wide diversity in
metallicity,
dust depletion, and ionization conditions, consistent with multiple possible origins. While a substantial fraction of this predominately ionized gas is consistent with the high-velocity extension of the LMC wind, part of it may arise from contamination by Milky Way (MW) high-velocity clouds (HVCs) and Magellanic circumgalactic medium (CGM). We estimate a nearside cool-gas
outflow mass of ${\sim}1.8\times10^{7}\,M_{\odot}$, implying $\dot{M}_{\rm out}\approx0.15$-$0.33\,M_{\odot}\,\mathrm{yr^{-1}}$ and a mass-loading factor of $\eta\approx0.6$-1.3. On regional scales, 30 Doradus contributes $\sim10\%$ and N11 contributes $\sim3\%$ of the total
outflow mass, while the trailing side contains more wind material than the leading side, consistent with ram-pressure stripping. These results provide the comprehensive kinematic and physical characterization of how
stellar feedback,
galactic environment, and foreground contamination shape the multiphase wind emerging from the LMC.
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All authors Suraj Poudel, April Horton, Kathleen A. Barger, Frances H. Cashman, Jo Vazquez, Andrew J. Fox, Nicolas Lehner, J. Christopher Howk, Scott Lucchini, Dhanesh Krishnarao, Sabra Catalano, Anders Ripley, Wanyan Yuan, Natalie Van Tol, Citlali Alcala, Jordan Elliott, N. M. McClure Griffiths, Elena D'Onghia, Jason Tumlinson, Ananya Goon Tuli, Jacco Th. van Loon, Julia Roman-Duval, Yik Ki Ma, Callum Lynn
Optics
Geometry-Controlled Polarization Photocurrents in Scalable PtSe2 Infrared Pixels
Eunice Y. Paik, Owen A. Vail, Madaline R. Marland et al. (+11 more)
Polarization-sensitive photodetectors provide multi-dimensional optical information beyond the capabilities of traditional intensity-based detectors. The noble metal dichalcogenide PtSe2 presents unique opportunities for tunable polarization detection due to its strong
spin-orbit coupling, material stability, customizable broadband polarization responses, and direct compatibility with a wide range of substrates for back-end-of-line silicon integration. In this work, we demonstrate room-temperature near-infrared to mid-wavelength infrared polarization photoresponses using scalable, as-grown, wide-area PtSe2 films, and we show that the measured polarization response is reshaped by device geometry. Finite-element current-flow simulations reproduce the observed spatial redistribution of the polarization-sensitive response and localize the transverse polarization response near the pixel center. This geometry-enabled separation allows wavelength-dependent
laser spot scans to distinguish
symmetry-allowed photocurrents from contact-proximate, dichroism-mediated photothermal contributions. At near-infrared wavelengths, we observe spatial response that is consistent with linear-dichroic photothermoelectric currents, whereas mid-wavelength infrared measurements reveal a helicity-dependent photothermal contribution under oblique illumination. These results identify pixel boundary engineering as both a design lever and a diagnostic tool for scalable PtSe2 polarization-sensitive infrared pixels.
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All authors Eunice Y. Paik, Owen A. Vail, Madaline R. Marland, William A. Beck, Antonio Llopis-Jepsen, Wendy L. Sarney, Jeffery H. Leach, Stefan Heiserer, Nikolas Dominik, Cormac Ó Coileáin, Paul B. Seifert, Georg S. Duesberg, Blair C. Connelly, George J. de Coster