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arXiv2026

In situ performance of the Vertex Silicon Plane in the BM@N experiment during Run 9

The Vertex Silicon Plane (VSP) was commissioned and operated for the first time as the most upstream tracking station of the Baryonic Matter at Nuclotron (BM@N) experiment at the NICA accelerator complex during Run 9. The station consisting of six double-sided silicon microstrip modules based on the CBM-BM@N detector technology was installed about 8 cm downstream from the target inside the SP-41 analyzing magnet. The in situ module performance was characterized in terms of the signal-to-noise ratio, time resolution, and Lorentz drift in the magnetic field. The most probable cluster signal-to-noise ratio ranges from 15.5 to 33.2, while the time resolution relative to the trigger pulse is about 12 ns. The tracking performance was evaluated using track-hit residuals and hit-matching efficiency; two independent reference configurations based on the Forward Silicon Detector (FSD) and Gas Electron Multiplier (GEM) tracking systems give consistent efficiencies of about 95%. The contribution of the VSP to the BM@N tracking performance was further studied through the transverse track impact parameter and the reconstruction of short VSP-GEM tracklets. Owing to its position close to the target and its coverage at large polar angles, the VSP provides an additional near-target tracking point and makes it possible to extend the geometrical acceptance beyond that of the FSD- and GEM-based central tracking system.

physics.ins-det↗
arXiv2026

Self-Supervised Representation Learning for JWST Galaxy Images and Low Resolution Spectra

A self-supervised multimodal model recovers galaxy stellar masses from sparse JWST data that lack the multi-band coverage required by traditional SED fitting. We train on single-band F150W imaging paired with observed-frame 1-2 $μ$m PRISM spectra and obtain a joint image-spectrum representation that recovers stellar mass at $1<z\le3$ with $R^2 \sim 0.9$ and $σ_{\mathrm{NMAD}} = 0.24$ dex; cross-modal CLIP alignment further raises single-modality performance by $ΔR^2 = +0.04$ (imaging) and $+0.09$ (spectroscopy), narrowing the gap to joint-modality inference. The code and documentation are available at \href{https://github.com/2003cy/neurips2026_ssl_jwst}{GitHub}.

astro-ph.GA↗
arXiv2026

The taming of 3-fold flops

This article overviews recent progress in understanding and classifying one of the most elementary of birational surgeries within algebraic geometry, namely 3-fold flops, through the development of a noncommutative version of singularity theory.

math.AG↗
arXiv2026

nnInteractive Agent: General-Purpose AI Agents as 3D Image Annotators

Interactive 3D segmentation models such as nnInteractive turn a few spatial prompts (points, scribbles, boxes) into accurate volumetric masks, but a human still does the annotation work: finding each structure, placing prompts, checking the result and correcting it. General-purpose AI agents can now interpret images, call tools and write code. We show that such agents can take over this work without additional training: the user makes a request in plain language, and the agent works out what has to be segmented, locates the targets, prompts nnInteractive, inspects the 3D result, corrects it and responds to feedback. Asked for 'the muscles used for chewing', an agent identifies and segments the masseters and pterygoids; asked to count liver lesions, it writes its own code to find candidates and splits a merged lesion on request. Our open-source nninteractive-agent provides nnInteractive as tools over the Model Context Protocol (MCP), together with a skill that encodes how experienced users prompt it. On a benchmark spanning CT, MRI, PET and micro-CT of humans, a mouse and an ant (14 images; 51 targets from organs and tumours to muscles, foot bones, vessel trees and an insect brain), Claude Code and Codex reach a mean Dice of 0.81 and 0.84 from the request alone; when told where each target is, both reach 0.85 and prompt nearly as effectively as an oracle that places prompts using the reference segmentation. A text-prompted 3D model (VoxTell) is more accurate on most standard radiological targets but less robust: it returns an empty mask for one of them and fails on the leg muscles, the foot bones, the mouse and the ant, where the agents remain accurate. Code: https://github.com/MIC-DKFZ/nninteractive-agent

cs.LG↗
arXiv2026

Cosmological Inference with Gravitational-Wave Dark Sirens and 21-cm Intensity Mapping: Forecasts for LIGO-Virgo-KAGRA with MeerKAT and SKAO

Gravitational waves (GWs) and 21-cm intensity mapping (IM) are emerging as complementary cosmological probes: GWs provide direct luminosity-distance measurements, while neutral-hydrogen (HI) IM traces the matter distribution in redshift space. Their synergy offers a promising avenue for precise measurements of the Hubble constant. Within a standard-siren framework, we perform a joint cosmological and population analysis using $\mathcal{O}(150)$ mock GW detections with SNR > 12, as projected for one year of observations at LVK O5 sensitivity. We combine these with mock HI intensity maps from MeerKLASS and SKA-Mid, and study how observational limitations in both the GW and IM data affect the $H_0$ constraints. We find that uncertainty in GW parameter measurements is a dominant limitation on the cosmological constraints. Neglecting this uncertainty, the inclusion of HI information enables sub-percent constraints on $H_0$. We also find that observational effects in the HI surveys weaken the constraints, although they remain tighter than those obtained without HI information (spectral sirens). Despite accounting for HI IM observational limitations, including HI information reduces the $H_0$ uncertainty relative to the spectral-siren results by 61% for MeerKLASS and 53% for SKA-Mid. Because our results are based on a single realisation, they should be interpreted in light of possible realisation-to-realisation variability. Beam convolution most severely weakens the constraints. Instrumental noise can induce multimodality in the posterior, potentially biasing the inferred parameters. The results are sensitive to foreground under-cleaning and over-cleaning. Partial sky coverage has a relatively small impact. In the most realistic scenario, which accounts for both GW and HI IM limitations, we obtain $H_0$ precision estimates of 10% and 15% for MeerKLASS and SKA-Mid, respectively.

astro-ph.CO↗
arXiv2026

Potential estimates and improved Sobolev regularity for nonlocal fully nonlinear elliptic equations

This paper investigates pointwise and oscillatory potential estimates for viscosity solutions and their gradients to a class of nonlocal fully nonlinear elliptic equations. The key ingredient of our argument is to establish precise pointwise bounds for a novel fractional sharp maximal function defined in terms of affine functions. As an immediate consequence, we prove higher order Sobolev regularity results of Calderón-Zygmund type for such equations without imposing any global boundedness assumptions on viscosity solutions. The potential theory developed herein extends the work of Daskalopoulos-Kuusi-Mingione (Commun. Partial Differ. Equ. 39: 574-590, 2014) for fully nonlinear second order elliptic equations to the fractional fully nonlinear setting.

math.AP↗
arXiv2026

MQAScore: Fine-Grained Text-Music Alignment Evaluation via Large Audio Language Model

Text-to-music alignment is commonly evaluated by the global similarity between text and audio embeddings, which collapses all described attributes into a single score and obscures which ones are missing. We instead introduce MQAScore, which verifies each atomic musical concept along five clip-level dimensions (genre, instrument, mood/theme, vocal, and usage) by the probability that a large audio language model (LALM) answers affirmatively to a binary question. To assess evaluator reliability, we construct verification labels from presence/absence annotations and LLM-guided concept substitutions, and propose the Sensitivity-Invariance Ratio, which measures how selectively an evaluator responds to meaning-changing substitutions. Experiments show that concept-level scoring improves both question-answering and similarity-based evaluators, and MQAScore can be a more reliable and interpretable fine-grained complement to global similarity for evaluating text-to-music alignment.

cs.SD↗
arXiv2026

Nitrogen vacancy cluster-mediated ferroelectric domain growth in wurtzite AlN

Aluminum nitride-based ferroelectrics combine high remanent polarization, thermal stability, weak size effects, a wide bandgap and back-end process compatibility, making them promising for high density non-volatile memory. However, their high coercive field ($E_\mathrm{c}$) and unclear polarization switching mechanism limit further applications. Theoretical predictions indicate preferential reversed domain growth along the polar axis, whereas experiments show nearly isotropic growth or preferential growth perpendicular to this axis. Here, we combine density functional theory, Deep Potential molecular dynamics and experimental characterization to determine how nitrogen vacancies ($V_\mathrm{N}$) regulate domain growth and $E_\mathrm{c}$. In ideal crystal, strong lattice coupling along the polar axis drives preferential domain growth in this direction. $V_\mathrm{N}$ locally weakens this coupling and promotes polarization nucleation. The spatial distribution of $V_\mathrm{N}$ and the temporal sequence of vacancy induced switching jointly determine the direction and morphology of reversed domain growth. We further show that scandium doping promotes $V_\mathrm{N}$ formation, thereby enhancing defect mediated nucleation and reducing $E_\mathrm{c}$. These findings establish a multiscale mechanism governing thin-film domain-growth kinetics and macroscopic $E_\mathrm{c}$, reconciling experimental observations with ideal crystal simulations and providing defect engineering principles for low-voltage, reliable and scalable ferroelectric devices.

cond-mat.mtrl-sci↗
arXiv2026

Euler characteristic and flat cohomology of convex projective $4$-manifolds

Let $M=Ω/Γ$ be a closed properly convex real projective $4$-manifold. We prove the Chern-Hopf-Thurston conjecture for this class of manifolds, i.e. $χ(M)\geq0$. The argument transfers Akagawa's double-form identity on the Cheng--Yau cone over $Ω$ to a Bochner identity on $M$, from which we deduce that $H^q(M;Λ^pE^*)=0$ whenever $q<p(n+1-p)/(n+1)$, in arbitrary dimension $n$, for some flat bundle $E$ naturally attached to $M$. In dimension four, this implies that the cohomology with coefficients in $Λ^2E^*$ concentrates in degree two.

math.GT↗
arXiv2026

Ledrappier-Young entropy formula for $C^1$ diffeomorphisms with dominated splitting Part 3: full formula with arbitrary multiplicities

We establish the full Ledrappier-Young entropy formula for ergodic invariant measures of $C^1$ diffeomorphisms when the positive Oseledets bundles and their nonpositive complement form a dominated splitting. We prove transverse formulas under three-block domination and equality of metric and unstable entropy under positive-nonpositive domination. To complete the proof, we develop a new mechanism for estimating partial entropy through comparisons of conditional information along orbits. Applications characterize vanishing transverse dimension, give upper pointwise dimension bounds and exact dimensionality of hyperbolic measures. In the quasi-isometric-center setting, this implies a $C^1$ invariance principle for measures with nonpositive center Lyapunov exponents.

math.DS↗
arXiv2026

I$^2$-KAN: Interpretable Intra- and Inter-Modal Multi-Pathway Representation Learning for Multimodal Sentiment Analysis

Multimodal sentiment analysis (MSA) aims to infer sentiment by integrating linguistic, acoustic, and visual information. However, many fusion methods integrate modality-specific representations and cross-modal interactions into joint representations, making it difficult to determine whether predictive utility arises from a modality itself or from its interactions with others. More fundamentally, a modality's standalone predictive utility may not faithfully reflect its interaction-conditioned predictive utility. To address this issue, we propose I$^2$-KAN, an interpretable multi-pathway framework that explicitly maintains intra-modal and pairwise inter-modal information in separate structural pathways. Each pathway is refined by a Task-Decoupled Linear-Gated Denoising Bottleneck (TDL-GDB) to learn compact and task-relevant representations, followed by structured Kolmogorov-Arnold Network fusion that retains explicit pathway associations and supports multi-level interpretation. Extensive experiments on CMU-MOSI, CMU-MOSEI, and CH-SIMS v2 demonstrate strong overall performance. Ablation and interpretability analyses consistently show across the three benchmarks that low standalone predictive utility does not necessarily imply low interaction-conditioned predictive utility: a modality that appears weak in isolation can remain informative through pairwise interactions. These findings highlight the interaction-dependent nature of multimodal utility and suggest that modality utility should be characterized from both standalone and interaction-conditioned perspectives.

cs.CV↗
arXiv2026

A sharp isoperimetric bound for the ratio of the fifth and fourth eigenvalues of Dirichlet Laplacian

Let $Ω\subset\mathbb{R}^n$ be a bounded domain with $n\geq2$. The well-known Payne-Pólya-Weinberger conjecture for consecutive eigenvalue ratios asserts that $$ \frac{λ_{m+1}(Ω)}{λ_m(Ω)}\leq\left(\frac{j_{n / 2,1}}{j_{n / 2-1,1}}\right)^2,\quad m=1,2,3,\cdots. $$ Here, $j_{p,k}$ denotes the $k$-th positive zero of the Bessel function $J_p$, and $λ_j(Ω)$ are the Dirichlet eigenvalues of $Ω$, counted with multiplicity and ordered as $$ 0<λ_1(Ω)<λ_2(Ω)\leqλ_3(Ω)\leq\cdots. $$ The cases $m=1,2,3$ were established by Ashbaugh and Benguria in their seminal works. In this paper, we give an affirmative answer to the Payne-Pólya-Weinberger conjecture for $m=4$ by combining a quadratic-form identity with a Brouwer degree argument. We also extend the corresponding spectral inequality to arbitrary bounded open sets in $\mathbb{R}^n$.

math.AP↗
arXiv2026

Transformers with CoT Discover Heavy-Ball Acceleration Through Training

Modern transformers often solve complex tasks by generating and refining intermediate reasoning steps. To develop a theoretical understanding of chain-of-thought (CoT) reasoning, a notable recent study by Huang et al. (2025) viewed transformers as algorithm executors, and showed that when transformers' CoT steps are supervised by a gradient-descent teacher, they can learn to implement gradient descent for in-context weight prediction in linear regression. In this paper, we study the same in-context weight prediction task but ask whether CoT reasoning can go beyond merely imitating the teacher algorithm. We show that, after initial supervision from a gradient-descent teacher, further trajectory-level supervision using the true regression weights leads the model to implement the Heavy-Ball method, thereby achieving acceleration over the original teacher. Notably, this accelerated algorithm emerges without supervision from any Heavy-Ball teacher. Our results provide a concrete theoretical example in which transformer reasoning can discover new algorithms through training, rather than merely imitate the algorithm used for supervision.

cs.LG↗
arXiv2026

What Pairwise Evaluation Misses: Reward Scores across Prompts

Reward models score responses for preference optimization, filtering and ranking, and pooling scores across prompts needs them to be comparable. Yet pairwise evaluation compares two responses to the same prompt, so any score component shared by a prompt's responses cancels and goes untested. We study this component by comparing between-prompt variation in model scores with the same variation in human ratings of the same responses. We propose a human-referenced audit, built from a between-prompt variance share, a sibling-rating regression and prompt substitutions, and apply it to eighteen released scorers and six matched training conditions. We find that scores cluster by prompt more than the ratings do: on HelpSteer2, six reward models have between-prompt shares of 0.34 to 0.64 against a human share near zero. Replacing the original prompt with a fixed instruction keeps substantial clustering but weakens agreement with prompt-level human ratings, so clustering alone does not show agreement with humans. Part of that variation is useful: subtracting prompt means lowers the helpfulness of globally selected responses, and scores stay sensitive to a wrong prompt even when training shuffles prompt means. We propose that reward evaluation check between-prompt variation, sensitivity to a wrong prompt and usefulness for selection separately.

cs.CL↗
arXiv2026

Finite Element Approximation of Rotating MHD-Boussinesq Flows with Nonlinear Power-Law Viscosity

We propose and analyse a fully discrete finite element approximation of the three-dimensional incompressible rotating MHD-Boussinesq system with nonlinear power-law ($p$-Laplace) viscosity. Conforming elements are used for the velocity and temperature, $\mathbf H(\operatorname{curl})$-conforming Nédélec elements for the magnetic induction, and a semi-implicit backward Euler scheme in time. The discretisation preserves the principal energy structure: the Lorentz and induction terms cancel exactly, while the Coriolis force remains energy neutral. This yields well-posedness and mesh-independent energy stability. The nonlinear power-law diffusion creates two main analytical difficulties. Since a uniform time-derivative estimate for the discrete velocity is unavailable, strong compactness is obtained through a time-translate argument and Simon's compactness criterion. The weak limit of the nonlinear diffusion is then identified by a Minty argument based on a discrete energy $\limsup$ inequality. Compactness and passage to the limit hold throughout the shear-thickening regime, while identification of a genuine weak solution is obtained in the Newtonian case and, in three dimensions, above an explicit threshold dictated by the Lorentz force rather than by convection. We further establish a priori error estimates without any mesh-time coupling condition. Three-dimensional numerical experiments confirm the stability and convergence behaviour predicted by the analysis.

math.NA↗
arXiv2026

Sharp CR Beckner-Onofri inequalities under high-order holomorphic moment constraints

We establish sharp Beckner--Onofri on the CR sphere $\mathbb{S}^{2N-1}\subset\mathbb C^N$, $N\ge2$, under vanishing holomorphic moments through degree $m\ge1$. The optimal coefficients are $\frac{1}{m+1}$. The function inequality admits a stronger form involving only the energy above degree $m$. We also prove a quantitative concentration estimate in the $1$-Wasserstein distance and show that every maximizing sequence has diverging energy and approaches the family of uniform measures on regular $(m+1)$-polygons. The proof combines subcritical minimization with rigidity of the constrained Euler--Lagrange equation, obtained from an exact radial energy identity and a Hardy space projection estimate. Finally, weighted ball automorphisms yield sharp inequalities without moment constraints, with scalar conformal, barycenter, and holomorphic Gram determinant corrections.

math.AP↗
arXiv2026

HARMONY: Hierarchical Anchor Retrieval on Manifold for Oblivious-source Machinery Acoustic Anomaly Detection

In standard acoustic anomaly detection (ASD), models are usually trained separately for each machine or domain using explicit metadata. However, in realistic deployments, machine identifiers are incomplete, unreliable, or simply unavailable. Thus, metadata-free machinery ASD asks a single model to monitor mixed machine populations without machine IDs. In this paper, we argue that the main failure mode is not a weak detector family, but representation entanglement. The heterogeneous normal modes overlap in frozen pre-trained feature spaces, making anomaly scoring and approximate retrieval unreliable. We study this problem directly and propose HARMONY (Hierarchical Anchor Retrieval on Manifold for Oblivious-source acoustic aNomalY detection), an anchor-guided geometric repartitioning framework that reorganizes mixed-source features into compact Voronoi regions and reuses this structure for hierarchical retrieval. On DCASE 2020, HARMONY improves mean AUC from 75.40% to 90.00% (14.60 percentage points) over the strongest unified baseline and from 83.90% to 90.00% over a strong foundation-feature baseline. On a single CPU, its hierarchical retrieval achieves a 7.8x speedup over exhaustive search with only a 0.20 percentage-point AUC drop. These results suggest that incorporating explicit geometric partitioning can improve both detection accuracy and retrieval efficiency for ASD. Code is available at https://github.com/Zzyh0208/HARMONY.

cs.SD↗
arXiv2026

Policy Evaluation and Policy Gradient for Continuous-Time Markov Regime-Switching Systems

We study policy evaluation (PE) and policy gradient (PG) for continuous-time stochastic control with Markov regime-switching. The main challenges are the coexistence of diffusion and regime jumps, the coupling of regime-dependent value functions, and the construction of model-free learning rules from the coupled generators. We establish a martingale characterization of PE that incorporates both Brownian and switching martingales, and extend martingale loss and orthogonality methods to this setting. We further derive a coupled PG equation and a trajectory-based gradient representation that, under an action-independent switching generator, avoids explicit knowledge of the system coefficients and transition rates. These results lead to offline and online actor-critic algorithms. We also establish convergence and study the finite-grid approximation required for implementation. Numerical experiments for a regime-switching linear-quadratic problem illustrate the proposed methods.

math.OC↗