Papers

We construct a family of scalar-closed, non-additive maximum sum-rank distance codes (MSRD) by switching norm components of a $\sigma$-rational normal curve and lifting the resulting point set through a linearized Reed–Solomon syndrome map. We characterize the admissible switches by a multiplicative stability condition on the norm classes. In particular, for $1 \leq n_i \leq m$, $N=n_1+\ldots+n_{\ell}$ and $2\leq\delta\leq N-1$, every partition of $\mathbb{F}_q^*$ satisfying a specific condition, referred to as Condition $(\diamond)$, yields a code in $\mathbb{F}_{q^m}^{N}$ of size $q^{m(N-\delta+1)}$ and minimum sum-rank distance $\delta$; the code is non-additive whenever a curve component is retained. For $\ell\geq2$ these appear to be the first non-additive MSRD codes in the literature, all previously known families with more than one block being $\mathbb{F}_q$-linear. Moreover, every code of the family has the same sum-rank weight distribution as an $\mathbb{F}_{q^m}$-linear MSRD code with the same parameters, although the geometry of the switched set distinguishes it from linearized Reed–Solomon codes. In the single-block case, an explicit rank isometry identifies the construction with the cone codes of Durante, Grimaldi and Longobardi.

In this paper we study the geometrical entities as Gauss and mean curvatures attached to the ruled normal surfaces associated with rectifying curves. A particular and special example of rectifying curves is also investigated, via its attached ruled normal surface. Our main result is the proof of the non-existence of rectifying curves that are simultaneously Bertrand curves.

The definition and quantification of fuel (or energy) poverty remain contentious, particularly within the English policy landscape. The current official definition - Low Income Low Energy Efficiency (LILEE) - systematically underestimates the condition in low- and middle-income households, effectively obfuscating changing energy affordability norms. This paper presents a sensitivity analysis of fuel poverty trajectories in Nottingham, UK, across competing definitions and diverging optimistic domestic efficiency upgrades) and pessimistic (energy price inflation) scenarios. Results demonstrate that LILEE overstates the efficacy of efficiency upgrades while failing to adequately reflect the impact of price shocks. To address these deficiencies, we propose the Temporal Equity Framework (TEF), a budget standard-based approach paired with a proportional energy expenditure indicator that captures shifting affordability norms more equitably. The TEF also introduces continuous expenditure-based depth indicators to evaluate the entrenchment of fuel-poor households (the fuel poverty gap) and the resilience of non-fuel-poor households (the fuel poverty buffer). We argue that responsive definitions which also recognise fuel poverty as a continuum of vulnerability, rather than a static, dichotomous state, are paramount to ensuring the equitability of energy transitions. Further, we suggest that the early identification of fuel poverty and spatial targeting of remedial resources could be markedly improved by adopting the TEF. We conclude that the adoption of a multidimensional budget standard-based definition is essential to facilitate a more accurate and just evaluation of energy transitions in England.

Music understanding often requires comparing excerpts and reasoning about relationships among songs, sections, and stems. However, existing large audio-language models (LALMs) and music question-answering datasets typically operate on single recordings or compare independently sampled tracks with no known production relationship. We introduce STEMMA, a multi-audio music question-answering framework built around production provenance: whether excerpts originate from the same track or section, and which stems belong to which mixtures. Because such relations are sparse under conventional audio-first sampling, STEMMA adopts a relation-first construction strategy: it first specifies a target relation and then queries the catalog for excerpts that satisfy it and hard negatives that do not. Labels are determined directly from catalog provenance rather than generated by a language model from metadata. We build STEMMA-Bench for evaluation and a track-disjoint training set, STEMMA-Instruct. Fine-tuning two LALMs on STEMMA-Instruct improves multi-audio reasoning, with the largest gains on structural relations directly determined by the catalog, while preserving single-audio music understanding.

Earth system models (ESMs) have grown tremendously in realism, yet key uncertainties persist in the climate response to greenhouse-gas forcing, particularly due to cloud radiative feedbacks. In addition, their software architecture was not designed for accelerator hardware or modern artificial intelligence (AI). Here we present legoESM, a composable, differentiable, multiscale ESM written in JAX. It builds on decades of community-developed parameterizations and numerical methods, recast in a unified framework by AI coding agents under a human-specified scientific contract and verified through benchmarking. Dynamical cores, physics schemes, grids, complexity levels and components are swappable like building blocks, and can use conventional physics or machine-learned emulators. A single code base spans metre-scale large-eddy simulation to global simulations and weather to climate. End-to-end differentiability enables gradient-based calibration, variational data assimilation and online training. legoESM modular architecture enables systematic evaluation of diverse model variants to explore structural uncertainty and test hypotheses. legoESM produces realistic simulations across scales, reduces land-surface temperature bias through gradient-based calibration, and scales efficiently on GPUs to kilometer-scale simulations. It offers an open, community infrastructure for hypothesis testing, research and teaching in Earth sciences and a template for multiscale physical systems.

Predicting the finite-temperature stability of a disordered phase requires its free energy. It is traditionally approximated by combining the energy of a special quasirandom structure (a small cell mimicking a random alloy) with the ideal configurational entropy. This approximation neglects the short-range order that develops on cooling. In this study, we show that the conventional approximation is the first term of an infinite expansion of the free energy in energy cumulants. Higher-order cumulants are estimated from energies of random arrangements, without Monte Carlo or molecular dynamics. In a nine-element refractory system, adding the second cumulant reduced free energy errors by about an order of magnitude. The expansion gives phase diagrams with order–disorder transitions, defect concentrations, and short-range order. To demonstrate its utility, we used a foundation interatomic potential to screen lithium-excess rocksalt oxides across 26 elements for synthesizable disordered phases rich in the Li$_4$ clusters needed for lithium percolation. The approach applies to any lattice and chemistry, and brings disordered phases within reach of routine screening.

Recent LHAASO observations reveal ultrahigh-energy (UHE) gamma-ray emission from Cygnus~X-3 with evidence for orbital modulation, providing a rare opportunity to study particle acceleration and transport on binary scales. We develop a common binary–jet model that jointly explains the contemporaneous GeV–PeV spectra and orbital light curves. The GeV emission is produced by anisotropic inverse-Compton scattering of stellar photons by relativistic electrons, while multi-PeV protons escaping from the inner region produce TeV–PeV gamma rays through photohadronic and hadronuclear interactions. The GeV orbital modulation constrains the binary–jet geometry, allowing the UHE observations to probe the escaping proton population and its interaction with the circum-binary environment. We find that the UHE emission is strongly regulated by the accretion-driven wind structure. In the present state, a fast disk wind displaces much of the denser Wolf–Rayet (WR) wind from the escaping-proton trajectories, suppressing hadronuclear emission. Changes in the strength, collimation, or orientation of the disk wind can expose the escaping protons to a much denser WR wind and enhance the PeV gamma-ray luminosity by orders of magnitude. This provides a possible connection to the much brighter, though unconfirmed, PeV activity reported in the 1980s, and links UHE gamma-ray activity to the accretion and outflow state of the binary.

As part of a PhD thesis entitled `Scalar perturbations in warm inflation and during reheating' we present a software for computing warm inflation observables. In particular, our Mathematica implementation computes the power spectrum, spectral tilt, and tensor-to-scalar ratio for a given momentum scale. Compared with other implementations, we start in a Bunch-Davies state deep inside the horizon, ideally at a time when thermal noise is exponentially suppressed. We integrate gauge-invariant equations for three curvature perturbations across horizon exit. We continue deep enough outside of horizon so that all curvature perturbations agree. Results are illustrated for Standard Model embedded warm inflation, and we also provide notebooks for several other popular potentials and friction coefficients. The theoretical foundations for the code can be found in the main part of the thesis or in earlier papers [1,2]. Specifically, part II derives gauge-invariant, model-agnostic evolution equations, as well as the noise autocorrelator interpolating between quantum and classical domains. Part III presents the general ideas behind the numerical implementation, while part IV presents selected results. The code is described, line-by-line, in Appendix A. The published PhD thesis is available at https://doi.org/10.48620/101166 while the notebooks can be downloaded from https://github.com/alicarogeljblackhole/Warm-Inflation.

We extend the theory of De Giorgi-Nash-Moser to elliptic equations with symmetric coefficients $\mathbf{a}(x)$ which are possibly degenerate and unbounded but satisfy a coarse ellipticity condition. We prove local upper bounds for weak subsolutions, a weak Harnack inequality for nonnegative supersolutions, and a Harnack inequality for nonnegative solutions. The coarse ellipticity hypothesis requires spatial moments of coarse-grained matrices, suitably discounted and summed across scales, to be finite. In particular, it holds if, for some $\alpha,\beta\geq0$ and $1<p,q<\infty$, $$\mathbf{a}\in W^{-\alpha,p}\cap L^1, \quad \mathbf{a}^{-1}\in W^{-\beta,q}\cap L^1 \quad\text{and}\quad \frac{\alpha+\beta}{2}+\frac{d-1}{2}\Big(\frac1p+\frac1q\Big)<1.$$ We show that the coefficient range is sharp, including its boundary, in every dimension $d\geq3$, for $\alpha=\beta=0$ and for the corresponding Besov-type quasi-norms of negative order when $\alpha,\beta>0$. For $\alpha=\beta=0$, it corresponds to the results of Bella and Schäffner [8].

Accurate prediction of temperature-dependent elasticity is important for assessing refractory carbides under high-temperature conditions, but the computational cost of ab initio molecular dynamics (AIMD) limits systematic investigations across compositions and temperatures. Universal machine-learning interatomic potentials (uMLIPs) offer an efficient alternative, yet their accuracy for this task remains insufficiently established. Here, we benchmark nine uMLIPs against consistent AIMD reference data for five binary and two high-entropy (HE) carbides between 300 and 1200 K. Elastic constants and the corresponding bulk, shear, and Young's moduli are obtained using stress-strain molecular dynamics, explicitly sampling thermal atomic motion and anharmonic effects beyond thermal expansion alone. We assess absolute elastic properties and normalized thermal softening separately. MACE-MH-1 achieves the lowest overall mean absolute percentage error (5.7%). MACE-MH-1 and DPA4-Mini reproduce thermal softening most accurately, with mean deviations of 2.5 and 2.3 percentage points, respectively. All models generally underestimate stiffness, with larger equilibrium volumes relative to the AIMD reference likely contributing to this trend for most models. C12 exhibits the largest model-dependent errors. The HE carbides are described with accuracy comparable to that of the binary carbides, indicating no apparent accuracy penalty from chemical complexity. Accuracy instead varies with transition-metal composition, with group-V carbides, particularly TaC, presenting the greatest challenge. These results identify promising pretrained models for finite-temperature elasticity in carbides and show why accurate absolute stiffness and thermal softening must be assessed independently.

Automated research systems support literature synthesis, ideation, experiments, writing, and peer review, but their evaluation is dispersed across tasks, benchmarks, and studies that are difficult to compare directly. We review this literature from the perspective of evaluation design and evidence, covering six targets: literature synthesis, research ideation, executable workflows, scholarly writing and communication, automatic peer review, and end-to-end research. We compare task construction, evidence sources, evaluators, and scoring procedures to explain the capabilities assessed by different designs. Our synthesis highlights three recurring lessons: output checks, process checks, and human studies provide complementary information; evaluator calibration is specific to the property being assessed; and resource budgets and attempt selection are integral to interpreting performance comparisons. We identify diagnostic evaluation designs and documented gaps in supporting evidence, and translate these comparisons into reporting and audit recommendations for specific evaluation settings. The survey helps readers navigate existing evaluations, select appropriate benchmarks, and design subsequent studies.

Generative models can now synthesize highly realistic images, simultaneously increasing the risks of misinformation and visual forgery. Therefore, detecting AI-generated images becomes more essential, and a reliable detector must generalize to unseen generators and stay robust to unseen perturbations in the wild. Existing detectors are typically trained on either independently collected real and generated images or aligned real-generated pairs designed to mitigate content bias. Building on aligned pairs, recent methods form a mixed view by replacing some patches of the real image with their generated counterparts. However, we find that self-attention lets real and generated patches interact, so the feature of each patch no longer reflects its own source alone. This contextual shift makes a per-patch source label an imprecise target. To this end, we propose Relative Patch Response Learning (PRL). Instead of labeling each patch, PRL compares the same patch across two mixed views of an aligned pair and learns from its patch response, the change of its score between the views. (i) To give precise supervision under the contextual shift, a relative response objective measures the responses of source-changed patches against those of source-unchanged patches, which respond to the shift alone. (ii) To provide a reliable reference for the shift, a reference coherence objective keeps each group of source-unchanged patches moving as a whole. (iii) Since the two views contain different amounts of generated content, an area ranking objective asks the view with the larger generated area to have a higher mean patch score. Extensive experiments demonstrate the superior performance of PRL, which surpasses the best prior methods by 4.3% and 5.9% in average balanced accuracy across eight standard and three in-the-wild benchmarks, respectively.

Commercial on-device network operating systems (NOSes) run the complex control planes of production routers and switches, where configuration update tasks are executed by multiple loosely coupled components through asynchronous message passing. Such executions are prone to race conditions: the same ordered input commands may produce different outcomes when messages are delivered in different orders. The race conditions are difficult to expose because they often manifest only as subtle, delayed malfunctions. Existing static analysis techniques lack scalability and precision for large-scale industrial NOSes, while dynamic ones incur substantial system-execution cost when attempting to cover the space of asynchronous message interleavings. To address the challenges above, we present NosRacer, a dynamic analysis framework for race condition detection in industrial-grade on-device NOSes. NosRacer uses a two-phase design. The concentration phase reduces analysis scope by leveraging the locality of configuration update tasks. Race condition detection is then limited to a small subset of involved components and crucial state variables, thereby reducing the detection cost. The perturbation phase proactively perturbs message asynchrony to increase the likelihood of executions with race-condition-exposing message interleavings. It keeps perturbation practical by grouping compatible perturbations for parallel execution and adaptively strengthening perturbations. We implement NosRacer in a commercial, actively developed NOS. NosRacer is integrated into the existing testing factory and used to detect race conditions in 5 key control-plane components. NosRacer achieves 66% precision and detects 21 race conditions confirmed by developers as severe bugs, while keeping the detection overhead below 10%.

We investigate the redistribution and directional properties of Gaussian tripartite quantum steering in de-Sitter space within the continuous-variable framework. By expressing the Bunch-Davies vacuum in terms of the open-chart modes through a Bogoliubov transformation, we derive the covariance matrix of the resulting multipartite Gaussian state and analyze both one-to-two and two-to-one steering configurations. We find that de-Sitter curvature generally suppresses the steering initially shared among the accessible modes, but its influence depends strongly on the steering direction. In particular, while some steering configurations undergo sudden death at finite curvature, two-to-one steering toward a nongravitational mode remains finite throughout the parameter range considered, demonstrating a robustness of tripartite steering absent in its bipartite counterpart. Remarkably, the maximum steering asymmetry occurs at the critical point at which steering in one direction undergoes sudden death, marking the transition from two-way to one-way steering. We further show that the de-Sitter gravitational field can generate tripartite steering involving modes separated by the cosmological horizon. Depending on the steering partition, this curvature-induced steering exhibits persistent one-way or asymmetric two-way behavior, as well as a sudden-birth transition from one-way to two-way steering. These results demonstrate that de-Sitter curvature not only degrades preexisting quantum correlations but also redistributes and generates directional multipartite steering across causally disconnected regions.

Secure deployment of FPGA bitstreams in heterogeneous multi-vendor cloud infrastructures requires scalable authorization, authenticated device access, and bitstream protection throughout the deployment lifecycle. Existing approaches typically address these functions through separate mechanisms, increasing coordination and key management requirements. This paper presents SAEID, a secure FPGA deployment framework that integrates aggregate authorization, certificate-free identity-based device authentication, and identity bound bitstream verification within a pairing based cryptographic framework, with symmetric cryptography used for session binding and AES 256 GCM based bitstream protection. Building on AgEID, an aggregate encryption scheme that enables individual decryption for authorized FPGA devices, SAEID extends the underlying framework to heterogeneous multi vendor deployments by supporting multiple FPGA vendors and IP providers, capability-aware authorization, and dynamic device membership. SAEID provides protection against unauthorized access to future deployments after device revocation and to prior deployments by newly enrolled devices, while retaining constant-size aggregate ciphertexts within each vendor domain and individual decryption. Experimental results demonstrate the practical performance of SAEID, with identity-based device authentication completing in approximately 4.35 ms and device membership updates requiring 4.95 to 5.09 micro seconds for device addition. The aggregate-encryption component exhibits scalable behavior with increasing device-set size. The complete SAEID software decryption path was also validated on a physical ZC702 Cortex A9 platform, requiring 191.126 ms. These results demonstrate scalable aggregate authorization with bounded authentication and dynamic-membership overhead for secure multi-vendor FPGA deployment.

We study bond percolation on the one-dimensional lattice in which two sites at distance $r$ are connected with probability $p_r=C/r^{1+\sigma}$, where $0 < \sigma < 1$. An infinite cluster exists if $C$ exceeds a critical value $C_c(\sigma)$, which is not known exactly: the available results are the lower bound of Schulman, $C_c\ge1/[2\zeta(1+\sigma)]$, and numerical estimates. Here we prove explicit upper bounds. We apply a second-moment argument to a family of random monotone paths whose steps have a heavy-tailed (Sibuya) distribution. Two such paths meet only a finite number of times, and their overlap is computed exactly by renewal theory. The result is a closed-form bound, which gives $C_c\le\sigma+O(\sigma^2)$ as $\sigma\to0$ and is below $1$ for $\sigma < 0.667$. Since the paths are monotone, the bound holds also for oriented percolation, and it determines the oriented threshold asymptotically: $C_c^{\rightarrow}\zeta(1+\sigma)\to1$ as $\sigma\to0$. A coarse-grained version of the argument, with blocks of sites in place of sites, gives an explicit bound $C_c < 1$ for every $\sigma < 1$. We compare the bounds with the known numerical values of $C_c$.

Long pulse operation in magnetic fusion devices requires well controlled plasma power exhaust to the divertor & wall, and avoidance of wall hot spots that could evolve in wall damage. At WEST, 10 major plasma facing components are monitored using 10 series of temperature/power indicators, based on multiple diagnostic systems, among which the infrared viewing system is especially relevant. These indicators span from the most basic ones (temperatures, power and energy from deterministic models) to advanced processes using artificial intelligence acquired through machine learning. Some advanced processes do operate in real time, and feedback on power actuators through the plasma control system, providing active control toward remaining within the safe operational domain. Other advanced processes intervene as forensic tools post discharge to identify possible dangerous situations regarding the power loading to the wall, so that the discharge run plan is adjusted to avoid running into aggravating wall events. No critical wall power event happened during the campaigns C9 to C11 (2024-2025), totalling about 13h of plasma, that would have affected the campaign plan. While it cannot be demonstrated that the active & intelligent wall protection enabled the new plasma duration record of 1337 seconds, the wall protection system as a whole plausibly contributed to obtaining these record durations by preventing wall hot spots to become critical during the campaigns.

Selection is a task that chooses one element from a finite public candidate range to maximize a data-dependent score. In differential privacy (DP), the exponential mechanism (EM) samples a candidate at a temperature calibrated to the global sensitivity. In this paper, we study when dataset-dependent sensitivity can safely replace global sensitivity in private selection. We propose three valid approaches. First, a private, high-probability upper bound on local sensitivity yields approximate DP, and the method extends to finite higher-order sensitivity hierarchies. Second, our Propose-Test-Release (PTR) variant privately searches a finite public grid for a temperature scale rather than fixing it in advance. Third, smooth sensitivity supports several designs. A candidate-independent smooth geometric construction produces a sensitivity envelope that is admissible under the local dampening framework, which privacy is guaranteed for any admissible envelope. Additionally, a separate logarithmic transformation utilizes smooth sensitivity to produce a smoothed candidate score function with advantages: having controlled global sensitivity, and preserving the maximizers of the original utility score, i.e., candidates maximizing the utility. Both of the designs yield range-independent pure DP. Besides that, we also give two approximate DP private selectors using smooth sensitivity: a direct EM with smooth sensitivity calibrated to the candidate range and privacy parameters that matches a theoretical lower bound up to some constant factor, and one using a privatized smooth upper scale by analyzing the logarithmic transform of the smoothness. For every proposed mechanism, we derive a high-probability regret bound under its stated conditions.

We consider the problem of learning structured linear dynamical systems over convex sets $\mathcal{K}$, where only a small subset of the observations are available at each time point. An estimator which minimizes a bias-corrected, potentially non-convex objective function is proposed. Non-asymptotic bounds are obtained for the statistical error, which depend on the local complexity of $\mathcal{K}$, the trajectory length $T$, and the sub-sampling probability $p$. Convergence of the projected gradient descent algorithm is also established. The general theory is applied to settings where (i) $\mathcal{K}$ is a subspace, (ii) $\mathcal{K}$ is the set of bi-isotonic matrices, and (iii) $\mathcal{K}$ is the set of matrices whose rows are formed by sampling Lipschitz functions. We show meaningful recovery of the transition matrix is possible for values of $T$ much smaller than what is required in the unconstrained case, and for $p = o(1)$.

While the Bloch sphere provides a canonical geometric representation for qubits, its generalization to pure qudit states ($d>2$) is not unique. This representation can be extended following two different approaches: increasing the number of points, as in the Majorana representation, or using a single point but in a space of larger dimension, as in the generalized Bloch representation. In this work, we compare these representations of pure qudit states by finding explicit analytical relations between them. In particular, a general formula of the Bloch vector in terms of the Majorana points of a given state is provided. We also analyze some suitable extensions of these representations in the case of pure permutation-symmetric two- and three-qubit states, deriving the corresponding relation between them. These analytical results allow us to study, from a geometric point of view, quantum correlations of special classes of two-qubit states.

We prove the existence and uniqueness of mild solutions to the ellipsoidal BGK (ES-BGK) model with the correct Prandtl number, under suitable weighted bounds and a free-transport non-vacuum condition. At the correct Prandtl number, the temperature tensor is no longer uniformly comparable to the scalar temperature, so classical scalar moment estimates do not directly yield the required Gaussian bounds. We derive anisotropic velocity moment estimates by splitting velocity space along the longest principal direction of the stress tensor and using the geometry of transverse elliptical slices. These estimates yield a linear weighted $L^{\infty}$ bound for the ellipsoidal Gaussian. Together with uniform ellipticity and weighted $L^1$-Lipschitz continuity under the stated assumptions, this bound allows us to construct unique mild solutions.

In deep learning, approximation theory motivates increasing representation size. We ask whether this benefit extends to dynamics learning through autoregressive prediction. We analyze the learned time evolution through the eigenstructure of Koopman operators, using relative residuals to detect spurious eigenpairs arising even as one-step error falls. For bounded Koopman operators, we show that minimal residuals over learned dictionary spaces converge pointwise to their full-space counterparts as these spaces approximate the observable space in $L^2$. Our hypothesis is that Koopman spectral reliability helps explain how consistently rollout error decreases with increasing dimension. We compare two models of a shared Koopman autoencoder trained alternately for reconstruction and latent evolution, using latent-prediction loss (one-step prediction errors in latent coordinates) or spectral-residual loss (relative residuals of candidate eigenpairs). Across six chaotic systems, both models reduced median windowed rollout error from smallest to largest dimension. The spectral-residual model achieved lower medians than the latent-prediction model for all systems and dimensions, and its median fell by a larger factor in every system. Its median decreased monotonically with dimension in four systems, against one for latent prediction. Against four baseline families, its mean valid prediction times were nearly always longer. At the largest dimension under two-stage training, we compared eigenvalue positions with each learned dictionary's residual contours. Spectral-residual eigenvalues concentrated in low-residual regions, whereas latent-prediction eigenvalues also appeared in high-residual regions, consistent with the hypothesis.

In quantum mechanics, among the proposals for how to compute the probability distribution of detection time and place along a given spatial surface or in a given volume, two leading candidates involve absorbing boundary conditions (ABCs) and complex absorbing potentials (CAPs) for the Schrödinger equation. Here, we extend earlier results on how the two are related. It was previously shown that ABCs arise as a limiting case of CAPs, but for that a (reflecting) Neumann boundary condition was assumed at the end of the region with the CAP. Here, we obtain ABCs in a different limit using a Dirichlet boundary condition at the end of the CAP region, which seems more practically relevant and realizable.

We show that the wild locus of an étale morphism of smooth adic spaces over an affinoid field is either empty or contains a divisorial point. As a consequence, we establish the equivalence of curve tameness and valuation tameness without using resolution of singularities. Moreover, given a finite étale map of regular schemes $f \colon Y \to X$ that is curve tame over a base $S$, we construct a compactification $\bar{f} \colon \overline{Y} \to \overline{X}$ over $S$ that is numerically tame.

Kernel Stein discrepancies (KSDs) provide a versatile tool for comparing distributions. One of their main applications is in quantifying the goodness-of-fit (GoF) between a data-generating distribution and a prescribed target distribution. In this work, we study the related problem of conditional GoF quantification: given only a (possibly non-normalized) conditional target model, without information on the distribution of its covariates, and samples from a joint distribution, the goal is to assess how well the conditional distribution of the samples matches the target. To tackle this setting, we present a framework that allows lifting unconditional KSDs to the conditional setting through an operator-valued kernel on the covariate space, going beyond the known Euclidean case. We establish that our suggested statistic vanishes if and only if the conditional model and the true conditional distribution agree for almost all covariates and deploy it to test conditional GoF on smooth manifolds and on discrete spaces. Our experiments on level, power, and runtime demonstrate the viability of testing on these domains using the proposed statistic.

Mathematicians value proofs for more than correctness: among correct proofs, simplicity, purity and the computational cost of finding them vary widely. Yet LLM-powered theorem provers largely search for any correct proof, and improve its quality only after it is found. We propose LEVER, a proof search algorithm that makes the objective over correct proofs programmable and optimizes it during search. LEVER scores partial proofs over an AND/OR proof graph, combining realized objective values with predictions for open subgoals, so the objective guides search before a proof is complete. The same mechanism optimizes computational cost, proof length, topical impurity, and even their weighted combinations, while the Lean kernel enforces correctness. On PutnamBench in Lean 4, under matched budgets, LEVER costs 34% less than a strong single-conversation agent while raising the solve rate from 80% to 96%. On reducing topical impurity, i.e., how far a proof strays from its theorem's subject, it improves over post-hoc refactoring (42% reduction against 33%) at two-thirds of the cost and more reliably; on proof length, the metric refactoring is built for, it approaches refactoring. Varying the objective's weights traces a quality-cost trade-off curve, so the user can choose how much a better proof is worth. Overall, LEVER is a performant, cost-efficient and tunable proof search algorithm for navigating the space of correct proofs.

One of the challenging components of modern lattice-QCD computations of the leading hadronic vacuum polarization contribution to the muon $(g-2)_\mu$ is the isospin-breaking correction due to electromagnetism. Dominated by long distances, this correction suffers from severe signal-to-noise issues and finite-volume effects. To provide infinite-volume benchmarks for various quark-level Wick contractions, we estimate their sizes phenomenologically at the physical point, using a previously developed vector-meson-dominance model. The pion contributions in this model sum to around $-7.1\times 10^{-10}$, dominated by the electromagnetic pion mass shift. The ultraviolet-finite (2+2)a ("dumbbell") contraction accounts for approximately two thirds of this model sum; for both, about 30% comes from Euclidean times beyond 2.8 fm.

Accurate covariance estimation is crucial for spatial data analysis. While parametric methods can suffer from model misspecification leading to wrong conclusions, nonparametric approaches are often neglected in practice as they rely on the estimation of a large number of covariance parameters and often face finite-sample bias issues. In this paper, we study the bias properties of sample covariance estimators for stationary lattice processes on $\mathbb{Z}^2$, when the true mean parameter is unknown and has to be estimated. We derive exact formulas for the finite-sample biases of sample covariance estimators and show that their expectations are linear combinations of population covariances determined by spatial lag and sample size. Based on this characterization, we propose jointly bias-corrected covariance estimators that are nearly unbiased. Additionally, we derive formulas for the mean-squared error and prove asymptotic normality results that show asymptotic equivalence for the estimators with and without bias correction. Simulations demonstrate substantial reductions of bias and often also in terms of MSE, particularly under strong spatial dependence. A kriging application to topography data further illustrates the practical benefits of the proposed approach.

Achieving and quantifying ultrastrong magnon-magnon coupling (USC) remains a key challenge for quantum magnonics. Here, we demonstrate widely tunable USC between chiral (right- and left-handed) and acoustic or optical magnon modes in the van der Waals antiferromagnet $CrPS_4$. Using a full quantum model, we decompose the interaction into three microscopic interaction channels: the co-rotating term $g_1$ (mode hybridization), the counter-rotating term $g_2$ (two-mode squeezing), and, uniquely in the chiral regime, the self-squared term $g_3$ that mediates single-mode squeezing. The normalized coupling ratio reaches $g/f_g$ $\sim$ 0.41, entering the USC regime. Most significantly, we establish a complete protocol linking these USC parameters to a measurable quantum phenomenon: a squeezed magnon vacuum state. Our simulations not only visualize the chirality and polarization evolution of the hybrid modes but also demonstrate how to directly extract quadrature fluctuations and a substantial squeezing factor (up to $\sim$ 9.7 dB) from thermal noise-driven magnetization dynamics. This work provides a material-specific quantum framework for USC and a practical pathway to detect and exploit non-classical magnon states in low-damping two-dimensional magnets, opening a route toward quantum-enhanced spintronics and hybrid quantum information platforms.

Agent skills provide reusable guidance for code agents, but incomplete or unsuitable guidance can impair task execution. To reduce the manual effort of skill refinement, recent approaches use LLMs to generate revisions from execution feedback. However, grounding these revisions in explicit behavioral evidence remains challenging. To address this gap, we propose SkillMorph, a skill-evolution approach based on trajectory-guided fault localization in agent skills. Its core idea is to link execution evidence to specific skill contents before generating revisions. Specifically, SkillMorph compares failure and success evidence in abstracted trajectories across repeated runs and tasks, incorporating changes between evolution loops to identify suspicious actions. It then uses these suspicious actions to localize edit sites in the skills and generate corresponding revisions. Experiments on SWE-Skills-Bench and CannBot show that the skills evolved by SkillMorph consistently achieve higher trial-level accuracy and execution consistency than the original skills and those from four existing skill-evolution methods. We have also applied SkillMorph to automated kernel generation with an AI operator-development team, which has accepted 6 skill-revision pull requests.