Papers

Snapshot hyperspectral imaging maps a spatial–spectral datacube onto a two-dimensional detector, with recoverability depending on the datacube sampling regime, the scene prior, and the optical encoding. We study this co-dependence with algorithmic recovery and optical design optimization in a differentiable metasurface model by varying the spatial–spectral ratio and comparing average-coherence, mutual-information, and end-to-end objectives. For compressed imaging with three bands, optimization of single-parameter dielectric pillars produces lens-like designs with overlapping wavelength-dependent point-spread functions across the objectives tested. End-to-end reconstruction can mask this collapse on restricted training distributions, showing that reconstruction fidelity depends jointly on the optical encoding and scene prior. For simple nano-pillar meta-atom geometries, the optimized singular-value spectrum deteriorates as the datacube becomes more spectrally dominated, whereas a relaxed model with independent complex transmission at each wavelength reduces this dependence. These results identify restricted wavelength-dependent transmission control in the pillar library as an important contributor to the observed spectral collapse. This motivates an illustrative local super-pixel spectrometer model in which spectral encoding is studied separately from global image formation under a plane-wave illumination approximation.

Large language models (LLMs) are increasingly used in coding tasks, but their ability to reason about code execution remains unclear. Existing repository-level QA benchmarks mainly evaluate static code understanding and often rely on LLM-based evaluation, while execution-reasoning benchmarks are mostly limited to snippets or functions. We introduce SWE-Flux, a repository-level benchmark for dynamic execution reasoning containing 480 execution-grounded instances across 12 real Python repositories, with gold answers automatically harvested from instrumented test executions rather than written manually or judged by LLMs. The benchmark covers singletest and multi-test questions over control flow, loops, program state, dataflow, exceptions, and program invariants. Evaluating five LLMs shows that this task remains challenging. The best model achieves only 37% accuracy. Models perform better on localized behavior such as invariants, intra-procedural control flow, exceptions, and simple loops, but struggle with dataflow, inter-procedural execution, precise state reasoning, and suite-level aggregation. Finally, we show that the oracle-harvesting pipeline can generate fresh benchmark variants using input perturbation. It successfully harvests valid variants for almost 90% of the selected instances, and the resulting variants are substantially more challenging for the evaluated models.

We study the nonequilibrium dynamics of a minimal recurrent transformer with $N$ normalized tokens, $Q=K=I$, and a negative value map $V=-I$. Similarity-based attention selects nearby representations, while the negative value map drives tokens away from the selected field. This feedback can continually reorganize both the representation geometry and the attention network. For $d=2$, the tokens lie on a circle, where the regular polygon is an exact fixed point. As the attention feedback strength $\gamma$ is increased, the polygon loses stability through a flip bifurcation, giving rise to period-two motion, chaos, and cluster-exchange or cluster-flip states. Despite this temporal complexity, attention remains diffuse as $N\to\infty$ at finite fixed softmax sharpness $\beta$. Attention condensation instead emerges in the scaling regime $\beta\sim N^2$. In the hard-routing limit, repulsive updates amplify local perturbations and routing-partner switches transmit them ballistically, producing an emergent butterfly cone in representation space. High-dimensional geometry provides a distinct route to localization. For $d=N\to\infty$, simulations from Gaussian initial conditions provide evidence for a condensation transition at $\beta=O(1)$, driven by dynamically generated finite overlap gaps. Depending on $\gamma$, the resulting phases include diffuse simplex-like states, consensus flips, condensed active routing with signatures of chaos, and fragmented cluster flips. These results establish temporal activity, attention condensation, and geometric clustering as distinct collective phenomena, and show that sparse attention can sustain persistent dynamics rather than freeze it.

For a convex body $K\subset\mathbb{R}^n$, let $w(K)$ denote the volume of its maximum-volume inscribed ellipsoid. We prove that every closed halfspace $H$ whose boundary passes through the center of the maximizing ellipsoid satisfies \[ w(K\cap H)\le\frac{\sqrt e}{2}\,w(K). \] The constant is optimal uniformly over all dimensions, as witnessed by a family of circular cones, thereby establishing Khachiyan's conjecture. The proof converts containment, maximality, and the central-cut condition into algebraic constraints on positive definite matrices. Two complementary spectral bounds from a diagonal model extend to arbitrary center displacements through a directional rank-one estimate for fractional trace powers. Concavity determines their joint optimum. We also derive finite-dimensional bounds and a necessary condition for near equality, with self-contained supporting proofs and an alternative resolvent argument. An AI language model discovered the proof in a human-directed research process. Lean 4 with mathlib verifies the main theorem, sharpness, and supporting results.

Spin-density wave (SDW) order and superconductivity frequently compete and coexist in unconventional superconductors, where spin fluctuations often mediate superconducting pairing. In iron-chalcogenide superconductors, FeSe$_{1-x}$S$_x$, SDW order has only been detected under applied pressure, while both spin and nematic fluctuations are involved in determining their rich superconducting phase diagrams. Here, we report evidence for an incipient SDW phase, within the nematic state of FeSe$_{1-x}$S$_x$, revealed in magnetic fields up to 68~T. Once superconductivity is quenched, we observe sharp upturns in longitudinal resistivity accompanied by anomalies in tunnel diode oscillator frequency response and torque anisotropy, consistent with a field-induced electronic order. Dominant low-frequency quantum oscillations reveal a small reconstructed Fermi surface, consistent with a field-induced SDW order. Direct experimental comparisons with a pressure-tuned nematic, analogue, FeSe$_{0.96}$S$_{0.04}$, demonstrate that SDW phases are stabilized within the nematic phase of FeSe$_{1-x}$S$_x$ via both chemical substitution and applied pressure. These findings reveal that by weakening nematicity, the SDW orders are stabilised, which promotes the dominant superconducting pairing mechanism in iron chalcogenides.

Easy-axis frustrated triangular lattice antiferromagnets provide an important playground for stabilising a wide range of exotic magnetic phases. The delafossite $2H$-AgNiO$_2$ offers a unique model system containing a lattice of localised ($S=1$) moments surrounded by a honeycomb of itinerant electrons. Below $T_{\rm N} =19$ K, the system exhibits collinear stripe antiferromagnetic order, whereas applied magnetic fields induce a cascade of transitions which has been proposed to contain a magnetic supersolid phase. In this study, we perform detailed angular and field-dependent torque measurements in static fields of up to 45~T on single crystal samples. The angular dependence of the torque displays a sawtooth-shaped signal close to the first supersolid phase, while near $T_{\rm N}$, an unexpected additional modulation emerges. On the other hand, the field dependence of the torque indicates the presence of four field-induced anomalies which evolve in distinct ways as a function of field orientation. To understand these complex behaviours and assess the role of local moments, we employ mean-field and Monte-Carlo calculations on a minimal spin model and construct comprehensive polar phase diagrams at different temperatures. We find that the angular dependence of the torque can be understood in terms of crossing different phase boundaries by field rotation, and we identify qualitative similarities between the experimental and theoretical polar phase diagrams. Our study highlights $2H$-AgNiO$_2$ as a rich anisotropic system that provides a robust example of how spin supersolid orders can manifest in angle-dependent magnetic torque.

We propose and analyze a fully discrete finite element scheme for the Beris-Edwards system of nematic liquid crystal dynamics, in which the incompressible Navier-Stokes equations are coupled to a gradient flow for the Landau-de Gennes Q-tensor. The scheme combines a linearly implicit formally second-order accurate backward differentiation formula in time with an incremental Chorin projection step for the incompressibility constraint, conforming finite elements in space, and the invariant energy quadratization approach with mass lumping for the nonlinear bulk potential. Each time step requires the solution of one linear system and one Poisson problem. We show that the scheme is uniquely solvable, that it preserves the symmetry and trace-free structure of the discrete Q-tensor and molecular field, and that it satisfies a discrete energy law without any restriction on the time step. Our main result is that, as the mesh size $h$ and the time step $\Delta t$ tend to zero subject to $h^{2} = o(\Delta t)$, the approximations converge along a subsequence to a weak solution of the Beris-Edwards system. The convergence proof addresses two difficulties: the projection method produces two velocity approximations, only one of which is uniformly bounded in $L^2(0,T;H^1_0(\Omega))$, and the coupling term $\mathcal{H}\nabla Q$ requires strong convergence of $\nabla Q$, which we obtain from the structure of the equation for $\mathcal{H}$ rather than from any discrete $H^2$-bound. Numerical experiments in two dimensions exhibit approximately second-order convergence in space and time, and reproduce the splitting of a $+1$ point defect into two $+1/2$ defects and the transport and deformation of a skyrmion induced by a constant pressure gradient.

For every $\rho$ in (0, 1/2), we construct an entire function F of order $\rho$ whose logarithmic derivative has zero as a deficient value. This disproves an old conjecture of W. H. J. Fuchs.

Reordering a set of mathematical rules without changing its meaning should preserve the correct answer, but must a model's internal representations stay invariant too? We investigate this question using synthetic multi-step function-composition problems, each presented under multiple rule orderings with the same correct answer. We measure accuracy and permutation signal-to-noise ratio (SNR), which quantifies how distinctly ordering patterns are represented relative to variation across problem instances. Across 16 language models ranging from 1B to 8B parameters, we find a pattern: models that solve reordered problems more accurately represent different rule orderings more distinctly. Layer-averaged permutation SNR is positively rank-correlated with accuracy in every synthetic setting we evaluate, with Spearman correlations reaching 0.86. These findings highlight a distinction between answer invariance and representation invariance: successful mathematical rule composition can accompany distinct internal representations between equivalent rule orderings. This motivates distinguishing answer invariance from representation invariance, and offers a representational perspective on mathematical reasoning beyond answer accuracy alone.

Quantum Reservoir Computing (QRC) exploits the rich dynamics of quantum many-body systems to process time-dependent information with high-dimensional state spaces. While neutral atom arrays offer a scalable platform for this paradigm, realizing intrinsic temporal memory without relying on external classical buffering requires precise control over the relaxation dynamics of the system. We address the necessity of specific non-unitary dynamics for enforcing fading memory while overcoming the lack of separability. This study simulates and empirically identifies the specific dynamical regimes required to maximize the computational capacity of the reservoir, addressing the amount of dissipation, the effectiveness of lying at the edge of quantum chaos, and that of time-multiplexing compared to the scaling of the physical size of the system. Here we show that controlled dissipation is strictly necessary to induce echo state property, fading memory, and separability, in neutral atom arrays. Computational performance increases at the edge of quantum chaos. The counter-intuitive residual memory provided by the unital phase damping channel is justified by introducing a model based on pure outputs. The consequent implementation enables the solution of complex non-linear tasks, such as the Mackey-Glass time series, with as few as $N=5$ atoms. We establish a rigorous framework for engineering dissipative quantum reservoirs required for intrinsic temporal processing on near-term quantum devices.

We determine the optimal universal coefficient in a reduction of multiple to binary quantum hypothesis testing. Specifically, for every finite ensemble in any Hilbert space dimension (finite or infinite), we prove that the error probability of the global pretty good measurement (PGM) is at most four times the sum of the optimal binary error probabilities. By constructing a family of regular-simplex ensembles, we further show that the coefficient four is optimal, even for arbitrary global measurements. This result improves on the pairwise bounds established by Cheng and Liu [arXiv:2606.06246 (2026)] and entails an explicit, sharp guarantee for the standard PGM itself. Our proof is also simpler: rather than constructing sequential measurements and applying a union bound, our proof relies on purely matrix-analytic techniques, combining a direct block Gram matrix analysis of the PGM error and a refined inequality between quantum Hellinger distance and Bures $\chi^2$-divergence. Our analysis also yields a refined, one-shot pairwise Chernoff bound and explicit sufficient number of copies for a desired discrimination error.

The adoption of CMOS sensors in mobile photography is frequently compromised by the rolling shutter (RS) effect, which introduces geometric distortions and motion artifacts. Particularly, recent rolling shutter with global reset (RSGR) mode, while mitigating some RS issues, also incurs major limitations, including reduced capture speed and compressed dynamic range. To address these problems, we propose a novel dual reversed scanning setup utilizing both RSGR and inverted RSGR views. This solution not only handles the inherent flaws of RSGR by synchronizing complementary exposures to balance the dynamic range across the frames but also introduces an effective method for HDR photosequencing under highly dynamic scenes. Our proposed network first accommodates row-wise complementarity and manages visual shifts by row-adaptive feature alignment. Subsequently, the hallucination module, built upon a correlation-guided mixattention block, integrates the mutually reinforced features to recover missing details. In addition, we construct a coaxial imaging system to collect a real-world dataset, enabling robust training and evaluation beyond numerical simulation. Experimental results demonstrate the twofold benefits of our solution in mitigating RSGR limitations and advancing HDR reconstruction techniques.

We study minimal-norm interpolation and $\ell_2$-regularized logistic-loss minimization for binary classification by univariate two-layer ReLU networks. We give complete geometric characterizations of the optimal classifiers in function space, resolving how the solutions depend on whether hidden-layer biases are included in the parameter norm. When biases are unpenalized, the minimal-norm interpolators are exactly the continuous piecewise-affine functions that hug every label switch and have kinks of the appropriate convexity. When biases are penalized, the minimizer is unique in function space, has exactly one kink in each intermediate same-label segment, and is therefore a sparsest positive-margin classifier. We further show that adding a free affine skip connection leaves these function-space solutions unchanged but fundamentally improves the parameter-space landscape: every KKT point of the constrained problem becomes globally optimal, whereas suboptimal KKT points can occur without the skip connection. We establish analogous global-optimality and geometric results for sufficiently weak $\ell_2$-regularization of the logistic loss. In the unpenalized-bias case, we identify an additional sparsity-like restriction, implying that most minimal-norm interpolators cannot arise as small-regularization limits of margin-normalized logistic-loss minimizers. Numerical experiments across varying dataset complexity and network width support the predicted landscape and sparsity phenomena.

Online information is increasingly consumed in video format. Much of this comes in the form of *raw video*: continuous footage taken on a cell phone, with a hand-held camera, or via CCTV, which is then directly uploaded to social media platforms and content sharing services. Whereas professional or even amateur-edited footage tends to feature scripted speech, chyrons, graphics, and metadata that help contextualize its subject matter, raw video typically contains none of these things, making it a much more challenging medium for information retrieval and machine understanding. To facilitate progress in this domain, we release MultiVENT-Raw, a multilingual collection of nearly 120,000 primarily raw videos (over 5,300 total hours), paired with 130 events and 222 event-centric queries, along with human-annotated video relevance judgments and human-extracted key facts for relevant videos. MultiVENT-Raw supports both a retrieval task—to identify videos in the collection relevant to a query event—and a generation task—to summarize event-related videos into a coherent report for a target user. We benchmark strong baselines on MultiVENT-Raw, showing both tasks to be challenging even for some of the latest multimodal models.

We investigate charge-density-wave (CDW) coarsening in a two-dimensional quasiclassical Holstein model following thermal quenches into the ordered phase. Although the staggered CDW order parameter is nonconserved, domain-wall motion remains constrained by conservation of the microscopic electronic charge. The simulations exhibit apparent growth exponents between $1/4$ and the Allen–Cahn value $1/2$. These apparent exponents are primarily accounted for by the crossover kinetics $\dot{L}=[D(T)/L][1+L_\times^2(T)/L^2]$, where $L_\times(T)$ is a temperature-dependent crossover length. At low temperature, nearly binary occupations require compatible wall segments to rearrange cooperatively, producing the $L(t)\sim t^{1/4}$ limit. Thermal broadening creates partially occupied interfacial sites that permit local curvature-driven motion and restore $L(t)\sim t^{1/2}$ at late times. Fits to the measured growth rate, a dimensionless rate collapse, and a long-time large-system simulation consistently support this crossover picture. These results show that a microscopic conservation law can generate long-lived anomalous coarsening even when the emergent order parameter is nonconserved.

A formal category theory is constructed (in the form of a proarrow equipment), encoding weak coherent enrichment over a monoidal model category $\mV$. We describe how basic categorical concepts formulated via the equipment translate back to enriched categories. We characterize Dwyer-Kan equivalences of enriched categories as $2$-categorical equivalences. Specializing to either the Kan-Quillen model structure on simplicial sets, or the Quillen-Serre model structure on topological spaces, we prove that the resulting formal category theory is equivalent to the one associated with the $\infty$-cosmos of quasicategories, thereby extending the formal approach to $(\infty,1)$-categories in the sense of Riehl-Verity to encompass both simplicial and topological categories. A notion of classifying object, formulated internally to the equipment of $\mV$-categories, leads to enriched versions of Quillen's Theorem A.

Adolescent Idiopathic Scoliosis is defined as a lateral curvature of the spine that develops during adolescence, without known cause. The condition can result in significant pain and disability, and often progresses rapidly during adolescence. The objective of this paper is to predict the progression of the condition in a temporal sequence from ages 9 to 24, as measured from a sequence of Dual X-ray Absorptiometry (DXA) scans. To this end, we train a transformer model that takes in the curve of the spine to predict curve progression. The model is trained using a large-scale synthetic dataset of spine curves and their time series, covering different curve types and different progression patterns. We show that the model is able to generalise from synthetic to real data by evaluating it on a dataset of real DXA scans covering multiple time points. We find that fine-tuning the model on real data gives a significant boost to performance. The model is able to accurately predict spine curve progression in both scoliosis and normal cases.

In this exposition based on a lecture series at the CIMPA School on Operator Algebras and K-theory, 2025, we highlight modern perspectives on noncommutative geometry using dualisable categories. To this end, we show that several categories naturally arising in functional analysis (derived categories of bornological and condensed modules), operator algebras (E-theory) and stable categories (noncommutative motives) are dualisable. This in particular leads to a definition of algebraic K-theory for analytic spaces. Furthermore, the dualisability of E-theory and motives leads us to pursue an analogy between topological and algebraic K-theory, inspired by assembly map (Baum-Connes and Farrell-Jones) conjectures.

This work introduces a spectral transfer formalism for nonlinear synchronisation dynamics to resolve how internal dynamical activity redistributes across network scales, moving beyond traditional global observables like the Kuramoto order parameter. By projecting Kuramoto phase dynamics onto the eigenbasis of the graph Laplacian, we construct a time-dependent transfer matrix and derive novel network metrics, including the spectral flux, which quantifies directional redistribution between structural dynamical scales rather than physical transport across nodes. Numerical simulations on modular and hierarchical networks reveal highly structured, intermittent spectral transfer episodes characterised by forward and inverse spectral cascades, directional reversals, and complex interaction geometries. Crucially, we demonstrate a clear separation between macroscopic coherence and microscopic spectral interactions, showing that highly organised, fluctuating internal redistribution dynamics persist even beneath nearly stationary and featureless global synchronisation states. This framework extends conventional synchronisation analysis and establishes a multiscale approach for interpreting network dynamics as an evolving process of spectral reorganisation.

Dexterous manipulation demands long-term foresight and rapid reactive control. Vision-Language-Action (VLA) models, while proficient in high-level reasoning, often lack a fine-grained understanding of physical dynamics and spatial perception. Conversely, World-Action Models (WAMs) typically suffer from high inference latency due to iterative generation. These deficiencies result in a critical temporal misalignment where the model's intent fails to adapt to rapid physical contact changes. To overcome this fundamental bottleneck, we propose LiMA, an asynchronous dual-system generative framework that systematically decouples intent planning from reactive execution. LiMA organizes computation into a multi-scale hierarchy: a slow system handles sparse long-horizon spatiotemporal intent generation, while a fast system focuses on dense high-frequency motion refinement. To align sparse intent predictions with dense action trajectories, we introduce a Latent Schrödinger Bridge Coupling mechanism that formulates refinement as an entropy-regularized probabilistic transport process. LiMA reduces inference latency by 45.8% compared with Cosmos-Policy via asynchronous decoupling. Evaluated across six bimanual dexterous manipulation tasks spanning multiple horizons, LiMA achieves an overall success rate of 70.8% and an average subtask success rate of 78.9%, while maintaining performance in unseen scenarios. The project website is available at https://ccdcs.github.io/LiMA_repo/

This work addresses continuous depression-severity score prediction from clinical interview transcripts under data scarcity. We propose a sequential low-rank adaptation (LoRA) protocol for cross-scale transfer: a Qwen3 backbone with a bounded regression head is first fine-tuned on the English DAIC-WOZ dataset (189 avatar-mediated sessions, PHQ-8), and the adapter then initializes fine-tuning on the Chinese PDCH dataset (100 real clinical consultations, HAMD-17), where a reinitialised, scale-specific head predicts the clinician-assigned score. All configurations use patient-level stratified 5-fold, 2-repeat cross-validation. On the data-scarce HAMD-17 target, the sequential protocol attains the best point-estimate MAE , RMSE, and macro-$F_1$ on both 0.6B and 1.7B backbones, outperforming target-only training and non-LLM baselines—4.96/6.59/0.36 with Qwen3-0.6B and 4.38/5.62/0.46 with Qwen3-1.7B. Ablations suggest that correctly aligned source supervision gives the best point estimates (unsupervised exposure and shuffled-label controls also show partial gains), that native-Chinese target input outperforms machine-translated English input, and that the reversed order yields no clear gain within run-to-run variance. The study is an exploratory, single-site internal evaluation: it does not establish screening or diagnostic utility, nor separately identify the contribution of the scale, language, or paradigm shifts. To our knowledge, no prior study evaluates this specific DAIC-WOZ-to-PDCH sequential transfer setting.

An always-on robot faces an endless stream that never resets: instructions arrive and lapse, the scene changes, and its own past actions reshape what it must reason about. Today's action models are built for the opposite: a fixed instruction, no mid-task intervention, single-step reasoning. In an open-ended world a robot must watch a live stream for far-future cues, recall its own far-past actions, and act on them under dual-arm concurrency. We present ARMS (Always-on Robot in Multi-modal Streams), a deliberately simple streaming policy: a single pretrained $\pi$0.5 backbone augmented by three lightweight modules that turn live perception, embodied states, and the robot's own past actions into context the backbone reads before it acts. The modules update this context asynchronously, so watching and recalling never block acting and the two arms act at once. Rather than inventing new mechanisms, ARMS integrates these learned context providers with an agent-causal self-history that logs which arm did what, and when. To supervise them without extra annotation, we build ARMS Dataset, whose staged construction script itself labels every module from real dual-arm teleoperation. Trained on it, ARMS reaches 45% on the combined task against 28% for the strongest of our four main baselines, and ablations confirm the memory module, the embodied-state head, and asynchronous concurrency are each necessary.

The role of surface gravity in neutron stars (NSs) is considerable in the radiation mechanisms of the surrounding plasma magnetosphere near the star surface, as they are highly magnetized, compact gravitating objects with compactness $M/R \simeq 0.2$. In this context, they serve as a celestial laboratory for testing gravity theories that dominate the stars' exteriors through plasma magnetospheric radiation. In this paper, we examine how dynamical Chern-Simons (dCS) gravity modifies pulsar electrodynamics in the slow-rotation, weak-coupling regime; the leading-order correction affects only the off-diagonal metric component $g_{t\phi}$, while the diagonal components remain as in General Relativity (GR). We first solve the Maxwell equations in the dCS framework for the electromagnetic field components and obtain analytical solutions for the electric and magnetic fields. We show that the magnetic field components are the same as in GR, while the electric field components are modified in dCS. We then derive analytic expressions for the induced electric charge density, known as the Goldreich-Julian (GJ) charge density, which sources the induced electric field arising from the magnetic field and the star's rotation. In dCS, it is larger than in the GR case, whereas the accelerating electric field parallel to the magnetic field lines is weaker. Next, we consider the deathline condition for switching off electron and positron radiation via inverse Compton scattering in the star's polar cap zone and show that the line shifts upward in the $P-\dot{P}$ diagram, explaining the physics of shorter-lived pulsars. Lastly, we study charged-particle acceleration in the polar cap region and show that electrons reach higher energies over shorter distances than in the GR case.

Personalizing exoskeleton assistance across operating conditions is constrained by the time and physical effort required to collect user feedback. We examined whether a user's preference landscape varies smoothly across operating conditions and when this continuity supports learning from limited feedback. We propose Context-Continuous Preference Learning (CCPL), a Gaussian-process preference model that shares observations across nearby contexts while retaining context-specific utility estimates. We evaluated CCPL through simulations and retrospective analyses of ankle and elbow exoskeleton preference data from nine healthy adults. In simulations, CCPL improved reconstruction and preference-based Bayesian optimization relative to independent learning when preferences varied smoothly, but showed negative transfer when continuity was weak. In both human studies, full-data reference landscapes estimated separately for each participant and context tended to be more similar between nearby operating conditions. With five exposures per context, CCPL increased mean reconstruction correlation with these references from 0.644 to 0.720 for ankle assistance and from 0.476 to 0.526 for elbow assistance relative to independent learning. The five-exposure budget was approximately 37% lower for ankle and 17% lower for elbow than the estimated independent-learning budgets needed to match these correlations. CCPL also improved held-out response prediction relative to independent learning, while benefits over pooled learning varied. These findings support context continuity as a basis for sharing preference observations under limited feedback, although benefits for online personalization in humans remain to be established.

Mechanical characterization of subsurface rock formations typically requires standardized cylindrical core specimens, which are often unavailable from fractured or unconventional reservoir sequences. This study uses a Discrete Element Method (DEM) framework calibrated to Sulphur Mountain Formation siltstone to investigate how fragment geometry governs mechanical response in irregular rock particles, which are direct analogues of drill cuttings. Nineteen specimens (18 procedurally generated irregular geometries and one reference Brazilian disk), normalized to a 10 mm bounding sphere radius, were tested under quasi-static (Brazilian-type) and dynamic (Short Impact Load Cell) loading modes. Four mechanical outputs of failure force (Ff), apparent strength ({\sigma}f), apparent stiffness (Ka), and stiffness (E) were regressed against seven retained shape descriptors. Results show that force-based quantities are strongly controlled by the surface-area-to-volume (SA/V) ratio under static loading (Adj. R2 = 0.69), while area-normalized quantities ({\sigma}f and E) are geometrically insensitive. Dynamic loading amplifies geometric sensitivity for failure force and introduces an independent role for surface concavity depth. These findings establish a preliminary quantitative framework for interpreting mechanical measurements from irregular rock fragments when a standardized core is unavailable.

Recursive state estimation often executes approximate numerical solutions inside a feedback loop, where highly accurate local steps do not guarantee better overall results. For a fixed linear Kalman model, we characterize when a correction within a prescribed subspace and norm budget can meet a local admissibility tolerance, and how the defects actually executed affect the finite-horizon covariance response. Centering each defect on the exact gain for the implemented covariance separates current solve error from inherited gain drift. Expanding the exact residual-drift identity reveals opposing quartic contributions beyond the quadratic response: innovation-covariance inflation enters positively, while local-gain reoptimization enters subtractively. Under matched initialization, an absolute sixth-order remainder bound, uniform over bounded defect sequences at fixed horizon, gives sufficient conditions for quadratic under- or overprediction. Machine learning proposes bounded corrections, while a learner-independent residual certificate and verified fallback govern execution of classical and quantum candidates without changing the reference estimator. In a power-grid tolerance study, learned correction lowers the minimum conjugate-gradient iteration count for deployment without fallback relative to uncorrected solves under the same residual certificate. Gains reconstructed from a variational quantum linear solver and from an annealing-based binary encoding, with small-scale terminal measurements on superconducting hardware and sampling on a quantum annealer, are executed through the same interface. By linking local repairability to nonlinear error propagation, the framework evaluates approximate solvers and learned corrections through independent certification and finite-horizon response, providing a practical basis for studying hybrid quantum–classical computation.

Catalog skin recolouring has to change pigment and leave shading alone. The classical Reinhard map does not make that split: it rescales lightness by the ratio of standard deviations, and a flat reference swatch therefore flattens the limb. This paper formalises the correction used in our pipeline, the skin-restricted Reinhard transform. It is the diagonal affine map in CIE Lab that translates lightness, matches the chromatic mean, and clamps the chromatic gain to [0.72, 1.18], with moments taken on the central 84% of each channel. A diagonal affine map has six real parameters. The shading constraint forces the lightness gain to +1 and the lightness shift to the difference of means; one-dimensional quadratic optimal transport on each chromatic axis, followed by Euclidean projection onto the gain interval, fixes the other four. Inside that family the four conditions determine every parameter. The content of the result is the forced lightness gain; it is not a uniqueness claim outside the diagonal affine class. For Gaussian marginals the chromatic step is not merely the best affine map: it is the unrestricted Wasserstein-2 map. The same formulae with trimmed moments remain optimal because a positive affine image commutes with quantile trimming. On hands, arms, legs, and feet of nine photographs and three reference tones, the map keeps the lightness contrast ratio at 0.974 +/- 0.029 with chromatic error 0.77 CIE Lab units. Reinhard matching, the linear Monge map, and histogram matching reach a smaller chromatic error only by cutting lightness contrast to about half.

This study examines the extent to which physics graduate teaching assistants (TAs) are aware of introductory physics student thinking and the types of challenges introductory students commonly have with energy and momentum concepts, which is important for implementing active learning methodologies and supporting diverse learners in physics courses. We present findings from a TA professional development course and discuss an approach to investigate TAs' pedagogical content knowledge, specifically their ability to recognize introductory student conceptual difficulties. We investigated 70 first-year graduate TAs' ability to identify common introductory physics student difficulties on the Energy and Momentum Conceptual Survey (EMCS). The TAs participated in a professional development course that emphasized reflection on introductory student thinking patterns to promote evidence-based pedagogical practices. TAs predicted the most common incorrect answers introductory students would select after lecture-based instruction, then compared their predictions with actual data from introductory students followed by a class discussion. Results reveal gaps between TAs' perceptions and introductory student thinking, with TAs performing poorly on many of the analyzed questions. For example, TAs consistently overestimated that introductory physics students would use novice-like thinking in many situations posed in EMCS problems, i.e., they expected introductory physics students to make more novice-like errors than they did. These findings have important implications for effective instructional design, e.g., physics TAs who misunderstand introductory physics student capabilities may inadvertently create barriers to learning by spending valuable class time on either over-scaffolding or under-challenging introductory physics learners and not spending time on pedagogical issues that are important to address.

Hybrid particle-in-cell simulations are widely used to study kinetic processes in collisionless astrophysical and space plasmas, yet the high computational cost of large-scale three-dimensional runs has largely confined production studies to two dimensions or restricted domains. To address this challenge, we present a performance-portable GPU implementation of the hybrid particle-in-cell code dHybridR. The implementation combines OpenMP target offloading with specialized SYCL kernels for the most computationally expensive operations, while preserving a unified CPU-GPU codebase that supports Intel, AMD, and NVIDIA GPUs. On the exascale supercomputers Aurora and Frontier, dHybridR achieves weak scaling efficiencies of $86\%$ to $97\%$ across 49,152 accelerators, and at 256 particles per cell, its full-node GPU throughput is up to $32\times$ that of the vectorized CPU implementation at approximately $90\%$ less energy per particle-update. To our knowledge, no other hybrid particle-in-cell code has reported GPU performance at this scale, leaving dHybridR uniquely positioned to exploit exascale systems. These advances substantially lower the computational barrier to large-scale three-dimensional hybrid-kinetic simulations of collisionless plasmas.

We investigate topological defects produced by a chiral phase transition in a fermionic ultraviolet completion of dynamical Chern-Simons (dCS) gravity. The model contains a complex scalar field with a chiral Yukawa coupling to fermions. Below the chiral symmetry breaking scale, integrating out the gapped bulk modes produces a gravitational Chern-Simons coupling which, we argue, modifies cosmic string solutions from the phase transition. The resulting corrected string metric is supported by a generalization of the Callan-Harvey fermionic zero mode solution, in which the null current generated by these zero modes provides a mechanism for parity violation. In the weak-coupling and weak-gravity regime, we derive the leading order-reduced dCS correction to this exterior metric. We also discuss the effective action description for generic string configurations in dCS gravity. The gravitational Pontryagin term provides the anomaly inflow required to cancel the gravitational anomaly of the chiral worldsheet theory.