Papers

We propose a rubric for assessing expressed clinical reasoning in model responses, drawing on three bodies of work: medical education assessment frameworks (ART, SCT, Key Feature Problems and OSCE); clinical LLM benchmarks (MedR-Bench, HealthBench, TIMER-Bench, DR. BENCH, PrIME-LLM and PatientSafeBench); and general LLM reasoning evaluation research, including the Factuality-Validity-Coherence-Utility taxonomy, FaithCoT-Bench and C2-Faith. We use groundedness as a clinically oriented adaptation of the taxonomy's factuality category. The rubric brings these concepts together in a multidimensional framework for scoring free-text responses to gold-standard clinical vignettes. It includes provisional behavioural anchors, applicability rules and a separate flag for case-specific safety-critical errors. General-domain frameworks inform its design but are not treated as validated clinical instruments. The rubric does not replace case-specific reference criteria or the task-specific metrics of existing benchmarks. It has not yet been tested for inter-rater reliability, construct validity or clinical utility. Its immediate purpose is to make evaluation decisions explicit and open to scrutiny before empirical testing.

Adam is widely observed to remain stable even when the objective deviates significantly from global smoothness. Under the generalized smoothness framework, however, existing analyses rely on strong tail assumptions on the stochastic gradients, such as almost-sure boundedness or sub-Gaussianity. Whether Adam converges on generalized smooth objectives under only second moment information on the stochastic gradients, without such concentration assumptions, was identified as an important open direction by Li et al. (2023). This paper gives an affirmative answer under fairly general conditions: such tail assumptions are not necessary. Building on the Adam self-normalization framework of Jin et al. (2026), developed for classical smoothness and bounded variance, we extend the stopping-time and de-preconditioning strategy to the $L_0$-$L_p$ generalized smoothness condition and a generalized second moment ABC condition. Even when the stochastic-gradient condition provides only second moment information that may grow along the trajectory, the stochastic trajectory of Adam remains in a locally well-behaved smoothness region, with stretched-exponential tail decay under bounded variance and global smoothness. Consequently, we establish high-probability convergence rate guarantees over the full range $p<2$, with confidence dependence of order $\delta^{-1/2}$, while the stepsize prefactor depends on $\delta$ only through a single logarithmic factor. We further construct a hard instance showing that, under only second-moment information, this $\delta^{-1/2}$-type confidence dependence is sharp. Finally, in the regime $p<1$, we combine the trajectory control with polynomial-growth estimates on rare events to obtain convergence rate guarantees in expectation.

Concept Bottleneck Models (CBMs) built on vision-language models such as CLIP represent a latent space as human-understandable concepts. These representations are unfaithful: related concepts are entangled, so individual scores do not reflect their intended meaning. We propose CHOQOLATE, an interpretable-by-design layer based on 2-additive Choquet integrals, which merges correlated concepts into compact nodes. Across four datasets, CHOQOLATE achieves a favorable accuracy-interpretability trade-off, with weight-sparse and semantically coherent nodes. A closed-form gradient derivation, backed by experiments, explains why Choquet layers drive this organization without explicit supervision. Choquet weights also map directly to Shapley values, which enables test-time intervention. On standard bias-mitigation benchmarks, suppressing spurious concepts after training performs on par with methods that require group annotations or retraining, while needing neither.

In this paper, we study the final data problem for the defocusing nonlinear Schrödinger equation (NLS) $$ i\partial_t u + \frac12\Delta u = |u|^p u $$ in weighted spaces $\dot\Sigma^s(\mathbb R^d):=L_x^2(\mathbb R^d;|x|^{2s}\mathrm{d} x)$. Let $s_c=\frac d2-\frac2p$. Under the scaling of the NLS, $\dot{\Sigma}^{-s_c}(\mathbb R^d)$ is the scaling-critical weighted space. In three dimensions, within the range of exponents considered in this paper, we show that the final data problem is locally well-posed for $s\geq -s_c$ and ill-posed for $s<-s_c$. This is opposite to the corresponding initial data problem, which is locally well-posed for $s\leq -s_c$ and ill-posed for $s>-s_c$. For the three-dimensional quadratic equation, we further obtain a unique global solution for every radial final datum in the critical space $\dot\Sigma^{\frac12}(\mathbb R^3)$.

Satellite observations, precomputed embeddings, and map products describe the same evolving Earth, yet are stored as independent, petabyte-scale data products. Their continued growth calls for compact representations of multiple products while preserving spatial and temporal detail. We introduce Planetary Feature Fields (PFFs), which exploit redundancy across data products by modeling them jointly as continuous functions of space and time at planetary scale. PFFs are spatially local explicit-implicit (hybrid) neural fields. Each field shares a factored feature volume—a decomposition of an explicit 3D grid with smaller factors—across products, while lightweight implicit decoders reconstruct individual products across multiple timesteps. PFFs reconstruct EO products over space and time more accurately than single-product fields at matched compression rates. At $1800\times$ compression relative to the uncompressed source data, reconstructed features retain approximately $90\%$ or more of the performance achieved with the original features on pixel-level segmentation, change detection, and patch-level classification tasks. PFFs can add new timesteps by extending their factored feature volumes and add new products by attaching new decoders, while leaving existing outputs unchanged. PFFs reduce end-to-end feature access latency by an order of magnitude relative to evaluated API and cloud-storage pipelines.

Photographic evidence is becoming increasingly vulnerable to forms of alteration and fabrication that existing legal and technical workflows are not well equipped to evaluate. Surveillance frames, dashcam stills, and phone photographs may be used to establish presence, sequence, causation, damage, or identity, yet contemporary generative systems allow non-experts to alter or fabricate such images through ordinary prompt-based interfaces. Existing image-forensics benchmarks provide important resources for face manipulation, classical tampering, and general synthetic-image detection, but they are not organized around the forms of visual evidence submitted in courts, the localized edits that can change what an exhibit appears to prove, or the consumer-tool threat model now facing the justice system. We introduce the CIFAR Synthetic Evidence Corpus for Detecting AI-Manipulated Images, a benchmark for evidentiary image authentication in court and justice-system contexts. The corpus contains 1,505 photographic items, including 720 authentic controls and 785 manipulated or fabricated images, spanning surveillance, dashcam, and consumer-photo imagery. Manipulations are organized into scene-condition edits, localized element edits, and full fabrications produced with contemporary generative systems. Each item is released with structured metadata covering source provenance, manipulation tier, subtype, generator, prompt template, and scene attributes, enabling controlled evaluation beyond aggregate binary detection. We also establish baselines with publicly available image-manipulation detectors, showing that current systems exhibit error profiles that remain problematic for evidentiary use. The dataset, prompts, metadata, code, and baseline evaluation scripts are released to support research on visual evidence authentication, information integrity, and trustworthy AI for the justice system.

Large language models (LLMs) have shown strong potential as training-free text encoders for long-context embeddings. Existing approaches primarily improve information flow under causal attention and typically construct embeddings by uniformly averaging all token representations. However, for long documents, such mean pooling can dilute salient semantic information with abundant redundant or weakly informative content. To this end, we propose SCSP, a training-free framework that leverages semantic compression for informative token selection in long-context embedding. Specifically, SCSP first partitions a document into sentence-aware chunks and appends a semantic compression prompt to each chunk. A prompt-isolated attention mask preserves information flow among document tokens while restricting each prompt to its corresponding local context. We then use the attention patterns elicited by these prompts to estimate token importance, select informative tokens, and aggregate their intermediate-layer representations into the final embedding. Extensive experiments on long-context embedding benchmarks demonstrate that SCSP can be integrated into both zero-shot and fine-tuned models in a plug-and-play manner, consistently improving their performance.

Estimating nonlinear properties of an unknown quantum state with restrictive experimental accessibility is a fundamental problem in quantum learning. We study the sample complexity of estimating the state moments $\operatorname{Tr}(\rho^t)$, allowing arbitrary adaptive single-copy measurements. While purity estimation has optimal sample complexity $\Theta(\sqrt d)$ at constant additive error, the optimal dimension dependence for higher moments has remained unclear. We resolve this question for every fixed integer $t\ge 2$: for any sufficiently small constant additive error, the optimal sample complexity is \[ \Theta\!\left(d^{\frac{\lceil\log_2 t\rceil}{1+\lceil\log_2 t\rceil}}\right) \] with constant success probability. The complexity thus follows a dyadic hierarchy: for each integer $h\geq1$, all moment orders $2^{h-1}<t\leq2^h$ share the same exponent. In particular, the third and fourth moments both require $\Theta(d^{2/3})$ copies. Our results also apply to multistate overlaps, weighted and partial-transpose moments, fixed-rank spectrum estimation, and distributed estimation of nonlinear quantities. We also establish an $\Omega(d^{1-1/t})$ lower bound for arbitrary nonadaptive single-copy protocols, matching the known upper bound and demonstrating an advantage from adaptivity for every $t\geq4$. Our upper bound uses adaptive state filtering to reduce higher-order moment estimation to lower-order moment estimation in a smaller state space. For the lower bound, we directly compare moment-matched ensembles through a smooth interpolation, bypassing the maximally mixed state as an intermediate hypothesis and yielding matching bounds beyond $\sqrt d$.

Hilbert C*-modules whose coefficient C*-algebra is equipped with a finite faithful trace generate Banach Gelfand triples. This provides a natural setting for the interpretation of Hilbert C*-modules as function spaces. In particular, when the modules are finitely generated and projective, their external tensor products interact well with projective tensor products. This allowed us to derive abstract kernel theorems for Hilbert C*-modules. As an application, we apply our results to Heisenberg modules and obtain new kernel theorems for time-frequency analysis.

Infrared (IR) large-sky surveys allow study of how localized star formation is, enabling searches for young stellar objects (YSOs) not only at the centers of known stellar nurseries but also across the Galactic plane. However, these spatially unbiased searches suffer from contamination, most notably from dusty asymptotic giant branch (AGB) stars characterized by long-period variability. Using time-series analysis, and taking advantage of the different variability timescales of YSOs against long-period variables (LPVs), we assess the level of contamination of one of the most spatially unbiased YSO catalogs (Spitzer/IRAC Candidate YSO, SPICY). Distinguishing between these two groups lets us draw more robust conclusions about the frequency of isolated YSOs in our Galaxy and their implications. We cross-match the SPICY and VIRAC2 catalogs (VVV/VVVX Survey), build near-IR light curves for common sources, and compute their periods and amplitudes. Contaminants are identified as sources with periodic flux variations with periods $P\geq 80\,d$ and amplitudes $\Delta K_{\rm s}\geq0.35\,\rm{mag}$. From $58\,737$ common sources, we identify $742$ SPICY objects as LPV contaminants based on their long-period variability, and identify $307$ high-confidence periodic YSO candidates exhibiting short-period flux changes consistent with cool spots. Near- and mid-IR amplitudes are correlated only among LPVs, suggesting a common pulsation origin. In addition, the spatial distribution of the identified populations further supports our classification, with LPVs preferentially associated with the bulge and YSOs at the lowest galactic latitudes.

With a view toward applications in Riemannian geometry, we explore coloop splitting properties of regular matroids. Nienhaus showed by classification in rank four that a regular matroid has a cocircuit whose deletion yields two coloops unless the matroid takes a particular form. In the latter case, one can split off any element of the ground set as a coloop. We reprove this using Seymour's structure theorem for regular matroids and prove an extension to matroids of ranks five and six. As an application to Riemannian geometry, we prove that the torus symmetry assumption in a recent result of Mouillé, Nienhaus, and the second author can be relaxed from rank ten to rank nine.

Let B be a plane curve which has simple normal crossings. We prove that, if B = B_1 \cup B_2 has two irreducible components with deg B_1, deg B_2 \geq 5 or deg B_1 = 4, deg B_2 \geq 7, and if B is general, then the associated algebraic exceptional set is empty. Based on this, we show that for a general plane curve B satisfying \bar{c}_1^2 - \bar{c}_2 > 0, the open surface \mathbb{P}^2 \setminus B is Kobayashi hyperbolic.

Monocular RGB video provides an accessible source of human demonstrations for upper-body robot motion, yet video-driven human-to-robot transfer remains challenging because body and hand motion are recovered at different spatial scales, human and robot kinematics differ substantially, and fine distal motion is difficult to preserve across embodiments. We present a geometry-preserving motion-retargeting framework that integrates unified body–hand reconstruction with morphology-independent geometric transfer. Frame-wise body estimates, video-level observations, and detailed hand evidence jointly constrain a single differentiable Momentum Human Rig (MHR) state, while transient hand artifacts are repaired in parameter space. The reconstructed motion is represented by arm-segment directions, elbow configuration, relative palm orientation, and bilateral wrist relations, and is realized on the target robot through multi-stage inverse kinematics and robot-specific hand adaptation. Within the broader system, Across-VAM provides video generation, whereas Across-WAM performs human-to-robot motion mapping. The method is evaluated on 16 monocular videos comprising 1,769 source frames, including 10 signing and six reach-to-grasp sequences. Unified reconstruction reduces mean hand reprojection error from 22.36 to 7.21 pixels relative to SAM 3D Body. All 16 retargeted trajectories completed kinematic simulation playback, and representative signing and reach-to-grasp motions were further demonstrated on a physical robot. The results demonstrate a unified pipeline from monocular human video to coordinated upper-body motion on a dual-arm dexterous robot.

Pretrained visual representations support image generation, but may not fully preserve the fine-grained details needed for faithful reconstruction. Meanwhile, intermediate encoder layers contain complementary visual details, but learning to fuse them for reconstruction can produce a latent distribution that is difficult to model. Existing fusion methods require empirical tuning of layer selection or staged optimization of fusion and decoding, increasing configuration effort or training complexity. We introduce HiRAE (Hierarchical Representation Autoencoder), which learns a hierarchical fusion framework over the full encoder hierarchy to improve reconstruction fidelity while maintaining compatibility with generative modeling. HiRAE groups encoder layers by depth and learns residual corrections to the deepest representation. Group-wise norm caps bound these corrections relative to the deep anchor, with tighter budgets for shallower groups. Our HiRAE-24 preserves the latent token count and channel dimension. On ImageNet-256, HiRAE-24 reduces reconstruction FID from 0.299 to 0.209 relative to RAEv2 while maintaining competitive guided generation quality. For text-to-image generation, HiRAE-24 improves alignment over RAEv2 on GenEval, DPG-Bench, and GenAI-Bench both before and after supervised fine-tuning. Under the same generator-training and evaluation protocol, post-fine-tuning GenEval increases from 84.86 to 87.70.

Let $G$ be a connected graph, and let $\lambda_1(G) > \lambda_2(G)$ denote its two largest adjacency eigenvalues. The spectral gap of $G$ is defined as the difference $\lambda_1(G) - \lambda_2(G)$. For integers $r\geq 2$ and $s\geq 0$, the double kite $DK(r,s)$ is formed by taking two vertex-disjoint copies of the complete graph $K_r$ and joining one specified vertex of each clique to a path with $s$ internal vertices. Stanić (2013) conjectured that every connected $n$-vertex graph with minimum adjacency spectral gap is a double kite. In this paper, we confirm this conjecture for sufficiently large $n$.

Artificial Intelligence Virtual Cells (AIVCs) are envisioned as scientific agents that simulate cellular responses, explain underlying mechanisms, and support hypothesis-driven discovery. Existing AIVC benchmarks, however, operate primarily at the simulation layer, motivating complementary evaluation of how models interpret experimental evidence and formulate biological hypotheses. We introduce OmniVCBench, a figure-centric, source-traceable benchmark for the interpretation component of an AIVC. It contains 6,077 curated single- and multi-subfigure question–answer pairs derived from figures and experimental contexts in the scientific literature. Guided by Bloom's taxonomy, we instantiate interpretation-layer counterparts of the AIVC Predict–Explain–Discover agenda through three scientific reasoning tasks. We further introduce AIVC-Judge, a task-conditioned MLLM-as-a-judge framework with category-specific, reference-aware rubrics for evaluating open-ended responses. A complementary Model-Derived Hard-Negative Mining (MDHNM) strategy converts plausible errors observed during model inference into MCQ distractors for lower-cost evaluation. Within the evaluated heterogeneous model pool, MCQ accuracy correlates positively with AIVC-Judge scores, providing a complementary view of performance alongside open-response evaluation. Code and data demo are available at https://anonymous.4open.science/r/OmniVCBench.

Diffusion and flow-matching Vision-Language-Action (VLA) policies generate action chunks through iterative denoising, incurring substantial inference latency that severely limits real-time robotic control. Existing acceleration methods treat an action chunk as a monolithic computational unit, ignoring a crucial physical reality of receding-horizon control: actions are generated jointly but consumed sequentially, resulting in inherently heterogeneous execution urgencies. We exploit this asymmetry to introduce Urgency-Aware Denoising (UAD), a novel inference-time framework that allocates denoising computation according to when each action is physically needed. UAD releases time-critical urgent actions after fewer denoising steps while overlapping the continued background refinement of tail actions with physical execution. However, heterogeneous denoising introduces two key challenges: early-release errors in urgent actions and trajectory inconsistency in tail actions. UAD elegantly resolves both through two core mechanisms: Trajectory Reconciliation, which reconstructs unified internal state evolution to restore joint denoising coherence without additional model evaluations, and Ghost Action Correction, which leverages non-executed ghost continuations to dynamically compensate for early-release errors across remaining executable actions. Extensive evaluations across multiple VLA architectures, simulation benchmarks, and real-world manipulation tasks demonstrate that UAD achieves up to a 1.89x speedup in average action availability latency while maintaining comparable success rates to vanilla inference with optimal denoising budget, offering a more favorable success-latency trade-off than state-of-the-art VLA acceleration baselines.

Simulated manipulation benchmarks are the standard tool for evaluating vision-language-action (VLA) policies and the acceleration methods that reduce their inference latency for on-robot deployment. On these benchmarks, we observe that some training-free acceleration methods, which approximate the baseline policy's computation, achieve higher measured success rates than the baseline itself. Success rates alone cannot establish whether such gains come from better task execution or from evaluation flaws. We therefore investigate two kinds of benchmark flaws behind these gains: bugs, where the implementation does not match the intended task or evaluation protocol, and design limitations, where success criteria and simulation settings do not fully capture how acceleration affects task execution. Starting from tasks with anomalous gains, we localize root causes by plotting object trajectories against checker acceptance regions, and classify the resulting bugs into task consistency, initialization, and reproducibility. Extending this audit to seven benchmarks, including RoboTwin, LIBERO-Plus, and VLABench, we identify 22 bugs of these types and 4 design limitations. For the latter, we revise permissive success checkers, correct unrealistic object masses, and add a motion-aware score that favors smoother actions. Experiments show that bug fixes can reverse method rankings, moving the baseline from last to first on one task. Addressing design limitations can likewise remove anomalous gains: on another task, the baseline moves from 21 percentage points behind an accelerated method to 5 points ahead. Gains attributed to acceleration can therefore be artifacts of the benchmark rather than better task execution. We release our bug fixes and revised benchmark settings to support trustworthy evaluation of VLA acceleration.

Gravitational wave (GW) astronomy offers unprecedented insights into binary black hole (BBH) coalescence. However, many of the key quantities involved remain inaccessible to direct observations. The BBH merger rate density is deeply linked to both the merger efficiency and the distribution of delay time between binary formation and merger, neither of which is directly constrained by observations. Disentangling their impact on the merger rate represents a highly non-trivial endeavour. Here we present a semi-parametric BBH population model, based on population synthesis simulations of both isolated and dynamically-formed BBHs, anchored on an observation-driven, metallicity-dependent star formation history. We parametrise the merger efficiency of these two formation channels, fitting the model to GW events from the Gravitational-Wave Transient Catalog 5.0 within a hierarchical Bayesian framework. Our analysis suggests that the isolated BBH merger efficiency should be lowered by a factor $\mathcal{O}(10)$ relative to standard population synthesis results. The dynamical channel requires an efficiency more than an order of magnitude larger than the isolated one to reproduce current GW observations. Nevertheless, we find that the two channels provide comparable contributions to the observed number of events. Finally, we introduce a parametrisation for the delay time distribution of the isolated BBHs. We derive a distribution consistent with the observed local merger rate and show its degeneracy with the merger efficiency.

Let $(M^{n+1},g)$ be a closed smooth Riemannian manifold, and let \[ 0=\lambda_0\leq\lambda_1\leq\ldots \] be the spectrum of the Laplace-Beltrami operator, with corresponding real eigenfunctions $\{\phi_j\}_{j\geq0}$. Let $\{\omega_p(M,g)\}_{p\geq1}$ denote Gromov's volume spectrum. In 2014, Marques-Neves conjectured that the sweepout generated by the nodal sets of $\phi_0,\ldots,\phi_p$ is asymptotically optimal for $\omega_p(M,g)$ as $p\to\infty$. We show that this conjecture is false in every dimension, even for positively curved real-analytic metrics. Nevertheless, we show that a less rigid notion of nodal sweepouts recovers the volume spectrum. Let \[ E_N(M,g):=\operatorname{span}\{\phi_0,\ldots,\phi_N\}, \qquad a_N\in H^1\bigl(\mathbb P(E_N(g));\mathbb Z_2\bigr) \] be the generator, and for $p\geq1$ define \[ \mathcal N_p^N(g) := \left\{ \Psi \mid X\text{ is a finite complex},\ \Psi\in C\bigl(X,\mathbb P(E_N(g))\bigr),\ \Psi^*(a_N^p)\neq0 \right\}. \] We define the nodal $(p,N)$-width by \[ \nu_p^N(M,g) := \inf_{\Psi\in\mathcal N_p^N(g)} \sup_{x\in\operatorname{dmn}(\Psi)} \mathcal H_g^{n}\bigl(\{\Psi_x=0\}\bigr). \] We prove the following filtration formula \[ \omega_p(M,g) = \lim_{N\to\infty}\nu_p^N(M,g) \] for every $p\geq1$. We state several questions on nodal geometry and min-max theory.

In this paper, we investigate the first-order one-loop quantum corrections generated by all possible nonminimal dimension-6 additive CPT-odd Lorentz-violating (LV) terms to analyze the radiative induction of the Carroll-Field-Jackiw (CFJ)-like terms. We demonstrate that for dimension-6 operators, the resulting CFJ term can diverge for some choices of LV operators; however, in all these cases, this divergence is eliminated for certain relations between LV parameters.

We derive nonlinear Zitterbewegung velocity of electrons augmented by band torsion in crystals. The equation of motion with multistate quantum geometric tensors and torsion culminates in transient nonlinear photocurrent responses distinct from the recently measured resonant steady-state photovoltaic effects induced by circularly polarized light. Tomography protocols for measuring the multistate quantum geometric torsion tensors are proposed.

Arrays of neutral atoms excited to Rydberg levels have emerged as one of the most promising platforms for quantum computation and simulation. With the hope to outperform classical devices, the number of atoms has been increased by orders of magnitude. However, the interaction time, i.e., the maximum accumulated time during which an atom interacts with its neighbours, has been limited to a few microseconds only. This restrains the number of gates per atom or prevents the simulation of long-time dynamics of quantum many-body systems. Here, we observe the spin-exchange interaction between two spin 1/2s encoded in laser-trapped circular Rydberg atoms over more than $60\mu s$ and 40 spin-oscillation periods, improving the state of the art by an order of magnitude. These unprecedented timescales allow us to record for weak atomic trapping a collapse and revival of the spin-exchange oscillation contrast induced by spin-motion coupling. Our results constitute the first observation of this coupling with laser-trapped Rydberg atoms. To counteract its detrimental effect for quantum simulation, we demonstrate a novel dynamical decoupling method that prevents the collapse of the spin oscillations. This method exploits the advantages of our recently developed hybrid platform that enables the measurement and the optical manipulation of long-lived circular Rydberg atoms with auxiliary Rydberg atoms. This work opens a direct route to long-duration quantum simulation of strongly-interacting many-body systems.

The Near-Ultraviolet eXplorer (NUX) is a proposed ground-based observing facility designed to expand near-ultraviolet (NUV) astronomy by enabling observations in the 300–350 nm range from Earth. The full system is intended to consist of four modified 36 cm Celestron RASA telescopes with custom NUV-optimized optics and UV-sensitive CMOS detectors, providing a total field of view of about 67 square degrees for high-cadence searches for fast, hot transients. To validate this concept, a single-telescope prototype, Proto-NUX, was constructed. Its optical design and development are described in previous work. Initial sea-level tests in the Netherlands showed that the instrument could be operated successfully and that the main technical requirements were met. In March 2026, Proto-NUX was deployed at the Pic du Midi Observatory in the French Pyrenees, at an altitude of 2877 m, for its first high-altitude on-sky commissioning campaign. The campaign tested the full system under realistic observing conditions, including deployment, remote operation, calibration procedures, detector behaviour, image quality, tracking, ghosting, and simultaneous optical monitoring. The observations demonstrate that Proto-NUX is a viable platform for ground-based NUV observations, but also show that the system was not yet operating at its expected optical limit. In particular, the delivered NUV point-spread function was broader than expected, with likely contributions from residual collimation error, defocus, chromatic effects, and internal reflections. The detector dark current was also found to be a significant contributor to the noise budget. We discuss these limitations and identify the main improvements needed for future Proto-NUX campaigns and for scaling the concept to the full NUX facility.

Computing spectra of differential operators on surfaces is crucial in many applications, ranging from medical image analysis to nanoscale quantum structures. However, discretization of the infinite-dimensional operator and the underlying surface can lead to inaccurate and misleading results. This paper introduces the SurfSpec suite of algorithms to compute eigenvalues and spectral measures of operators on surfaces with error control and convergence guarantees. We combine methods based on complex contour integration and residuals to compute discrete spectra and high-frequency eigenmodes, including of nonlinear eigenvalue problems. We then compute convolutions of spectral measures with rational kernels to deal with continuous spectra. In both cases, the key tool is the operator resolvent applied to functions, which is computed using high-order methods that solve surface PDEs. We illustrate our algorithms on a variety of differential operators and surfaces, including a triceratops.

Altermagnetic multiferroics provide a platform where non-relativistic spin-momentum locking (SML) coexists with relativistic spin textures, yet disentangling their different origins remains challenging. Here, using first-principles density-functional-theory calculations and symmetry analysis of the multipolar expansion of the spin polarization, we investigate the altermagnetic multiferroic BaCuF4. Its dominant non-relativistic altermagnetic d-wave SML originates primarily from a CuF6 octahedral rotation coupled to the polar distortion and can therefore be reversed by ferroelectric switching. We show that spin-orbit coupling generates additional spin multipoles and, depending on the Neel-vector orientation, induces spin canting and weak ferromagnetism. By exploiting the group-subgroup relations between spin groups and magnetic space groups, we then distinguish non-relativistic altermagnetic, canting-associated, and purely relativistic contributions to the SML. We further show that this hierarchy is encoded in the nonlinear spin-photogalvanic response, whose spin projection selectively probes contributions of different origins. These results establish a direct connection between the microscopic spin texture and nonlinear spin transport in altermagnetic multiferroics.

Basis-restricted priors in Bayesian inverse problems can lose coverage when the truth has components outside the basis. We show that estimating the observation-noise variance can hide this loss. Under a linear forward model, when the in-span prior variance dominates the noise, the maximum-likelihood noise estimate absorbs the out-of-basis energy in the complement of the model range. Residual-magnitude and observation-coverage checks then stay near nominal while field coverage falls. We study repeated problems sharing one forward operator and one basis, fixed independently of the tested data. After projection onto the complement, and conditionally on the fitted noise scale, every exact test is a test of the scale-free direction of the residuals. We test the shape of their sample spectrum with John's sphericity statistic. Under Gaussian noise its null model is exact at finite sample size, and we derive its null mean and its power at proportional dimension. On synthetic problems and in a preregistered GEBCO topography study, the test detects structured out-of-basis variation that cross-validation and observation-coverage checks largely miss. It cannot detect Gaussian out-of-basis variation that is isotropic in the complement, since that is indistinguishable from a change of noise scale.

We prove that the relative commutant of a finite unitary tuple in a tracial matrix ultraproduct is internal whenever its conjugation operator has a spectral gap off the commutant. This implies the existence of a non-hyperlinear group.

By performing a fit to the merged BES 2008 and BESIII 2024 $e^+e^-\to D\bar D$ cross-section data, we find that the $\psi(2\mathrm S)$ subthreshold pole influences this process markedly. The statistical significance of the $\psi(2\mathrm S)$ as a subthreshold pole is 8$\sigma$. A fit assuming it and seven resonances excels with the fit quality characterized by $\chi^2/\mathrm{DOF}=240.4/284$, which means a $p$-value of 97%. The interference of resonances with the continuum provided by the subthreshold pole changes their shapes, positions, and widths.

Vision-language models (VLMs) exhibit strong multimodal capabilities but remain vulnerable to backdoors implanted through poisoned fine-tuning data. Existing defenses often require extensive parameter updates during fine-tuning or incur per-query overhead during inference. To address these limitations, we propose Perturb-Select-Restore (PSR), a post-training defense that performs sparse updates to the projection interface and introduces no additional computation during inference. We reveal that backdoored VLM projectors are substantially more sensitive to bounded perturbations than clean VLM projectors, a phenomenon we term projection fragility. Building on this finding, PSR identifies the output channels most sensitive to perturbations in each projection layer of a backdoored VLM and restores their parameters to the corresponding pretrained values. Experiments across multiple tasks show that PSR reduces attack success rates to near zero while preserving clean-task performance.