Sparse Autoencoders (SAEs) have found success parsing neural representations into interpretable concepts, providing a basis for understanding and control. However, what exactly SAEs extract, and, correspondingly, the scientific conclusions we can draw from them, are not obvious. Empirically, the proof is in the pudding: SAEs learn interpretable features. Theoretically, we lack a clear account of what properties a 'concept' must satisfy for an SAE to extract it. There has been extensive identifiability work studying the conditions under which sparse coding recovers ground-truth features; however, these approaches tends to focus on simple data-generating models (e.g. sparse independent features) which poorly approximate the internet-swallowing language-model representations on which SAEs are trained. Here, avoiding data-generating models, we ask simply what properties any dictionary learning optimum must satisfy. Concretely, we extend local optimality analyses (Gribonval & Schnass, 2010) to the nonnegative joint-optimisation problem that vanilla SAEs approximate, and derive constraints relating optimal SAE features to their distributions. We use these constraints to explain a range of observed SAE behaviours - hierarchical splitting & absorption, the structure of residuals, and dense antipodal features - each reflecting how L1+nonnegativity interact with data to structure optimal dictionaries. Finally, we construct a novel large-dictionary convex problem and explore the wide atom-per-datapoint limit. In sum, we hope to tease model assumptions from unexpected observations, letting us learn more from SAEs' successes and provide principles for designing their successors.

Shapley values are a principled attribution measure widely used in interpretable machine learning, but their exact computation scales exponentially with the number of players, motivating a wide range of approximation methods based on value function evaluations of sampled coalitions. This raises the question of whether approximation accuracy can be improved by adaptively selecting coalitions for evaluation based on previous evaluations. This is particularly relevant in settings where the value function is costly and the number of evaluations is severely limited, such as retraining-based feature importance, data valuation, and hyperparameter importance. For this purpose, we propose ShaplEIG, a Bayesian experimental design approach that approximates the expensive value function using a Gaussian process surrogate and adaptively selects coalitions based on their expected information gain about the Shapley values. By the linearity of the Shapley values in the value function, we show that the expected information gain is available in closed form. Furthermore, we propose an efficient computation scheme that reduces the complexity from exponential to polynomial in the number of players via elementary symmetric polynomials. In extensive experiments across diverse costly applications, our method consistently improves sample efficiency in the low-budget regime over state-of-the-art baselines.

Probabilistic time series forecasting has attracted increasing attention in financial applications due to the need to quantify risk and uncertainty in future observations. We propose ProbRes, a post-hoc probabilistic calibration method that explicitly learns and incorporates volatility dynamics into probabilistic forecasting, enabling effective handling of heteroskedastic data. During training, ProbRes employs two architecture-agnostic modules to separately model the conditional mean and conditional volatility. At the inference stage, it generates predictive distributions by resampling normalized residuals. ProbRes is applicable to both univariate and multivariate time series and remains robust under a wide range of error distributions, including non-Gaussian innovations with conditional heteroskedasticity. Theoretical results demonstrate ProbRes's validity and experiments on both synthetic and real-world datasets show that ProbRes accurately captures predictive distributions and produces well-calibrated prediction intervals.

Biological image analysis increasingly demands integration across heterogeneous tools, programming environments, and domain knowledge that few researchers can command simultaneously. We present Agentic-J, a containerised, multi-agent AI assistant, primarily for ImageJ/Fiji that enables biologists to specify analysis tasks in natural language, from nuclei segmentation and cell tracking to multi-condition quantification. The agent generates executable scripts organised into a documented project structure, so every analysis decision is traceable and the workflow can be reproduced or shared. The specialised sub-agents handle plugin management, code generation, debugging, quality assurance, and statistical reporting. In this paper we introduce the system's design, demonstrate real biological microscopy image analysis workflows, and detailed the technical implementation.

We study exact community recovery in the two-community stochastic block model on $n$ vertices under limited and noisy access to network data. The learner may query a noisy neighborhood oracle that reveals each true neighbor of a queried vertex independently with fixed probability and never returns non-neighbors, subject to a finite query budget. We consider both oracle-only access and a combined model where the learner also observes a single subsampled copy of the underlying graph. For oracle-only access, balanced uniform querying gives a sharp non-adaptive benchmark: when each vertex is queried the same integer number of times, the observations reduce to an SBM with attenuated edge probabilities and the Abbe-Bandeira-Hall exact-recovery threshold applies. We show that this benchmark is not adaptively optimal: a two-stage adaptive strategy succeeds with $n+o(n)$ queries in a regime where balanced uniform querying requires $m n$ queries for some $m>1$. With an additional subsampled graph, we prove a sublinear-query adaptivity gap: balanced data-independent uniform querying with a sublinear budget does not improve over the subsampled graph alone, whereas adaptive querying can target a small set of uncertain vertices and achieve exact recovery. Thus adaptive data acquisition can strictly improve the information-theoretic limits of exact recovery.

Reconstructing spatially continuous daily temperature fields from sparse observations is important for urban climate monitoring and heat-risk analysis, but practical deployments are limited by sensor budgets and spacing constraints. This study proposes an uncertainty-aware graph neural network (GNN) framework for reconstructing daily maximum temperature fields from sparse sensors while supporting distance-constrained sensor placement and probabilistic exceedance mapping. The model predicts both the temperature field and a spatially varying predictive uncertainty field using a graph-attention-based mean-residual architecture trained with a Gaussian negative log-likelihood. Sensor placement is addressed using a Proper Orthogonal Decomposition with QR factorization (POD-QR) strategy with a 4 km minimum inter-sensor distance constraint and is compared with random feasible placement and farthest-point sampling. The framework is evaluated over a Montreal-area polygon using Daymet v4.1 daily temperature data (1 km resolution) under a strict temporal hold-out protocol (training: 2020-2023; testing: 2024). Across sensor budgets (10-40 sensors), the proposed GNN consistently outperforms inverse distance weighting and ordinary kriging in RMSE and MAE on unobserved nodes. Sensor-placement effects are most pronounced at low budgets and diminish at higher budgets, with a practical saturation regime emerging around 30 sensors under the imposed spacing constraint. Probabilistic evaluation further shows improved uncertainty calibration with increasing sensor density and a better sharpness-calibration trade-off than kriging. These results support the proposed framework as an effective tool for uncertainty-aware temperature field reconstruction and decision-oriented heat-risk mapping.

Pre-training has become a fundamental paradigm in modern machine learning, with one of its key empirical benefits being reduced downstream sample complexity as the scale of pre-training data increases. However, existing theoretical frameworks for pre-training do not fully explain this phenomenon. In this paper, we introduce complexity minimization, a novel meta-representation learning framework designed to enable theoretical analysis of this scaling behavior, which learns representations by evaluating the downstream model complexity best suited to each domain and minimizing the worst-case such complexity across source domains. Our end-to-end theoretical analysis, spanning pre-training through downstream regression, shows that this framework provably captures this scaling behavior; in particular, we show that the error rate of few-shot adaptation improves as the amount of meta-training data grows. Empirically, we demonstrate that incorporating complexity regularization into existing meta-learning methods consistently improves downstream sample efficiency.

Frontier LLMs increasingly decide what a query attends to with a sparse-attention indexer that picks a few KV-cache blocks per query: attention's unit is now a small, reusable chunk. Agentic workloads hammer it: many sub-agents query one large codebase, reusing the same blocks. When that corpus outgrows one GPU it is partitioned across instances, so a query and the blocks it selects often sit on different GPUs: answering it means attention across instances. The reflex of prior cross-instance KV systems is to move the cache: pull the selected blocks to the requester. Multi-head Latent Attention inverts the arithmetic, compressing each token's key and value into one narrow vector, so a routed query row is only ~1 KB, smaller than the chunk it attends; routing the query is then often cheaper than moving the cache. Which primitive wins, over which fabric and request shape, is uncharted, least of all on device-initiated RDMA that makes per-request cross-node transfers cheap. We characterize cross-instance MLA attention on a real multi-node H100 cluster, distilling two reusable artifacts: a topology-aware cost model (probe / transfer / compute / return / merge) and a closed-form route/fetch/local predicate, whose constants we measure on real IBGDA, where the model tracks batched round-trips to within ~7%. At decode it routes the query, trading the cost of moving the cache (a ~3 ms re-adaptation splice for a contiguous chunk, or a scattered gather under selection) for a tens-of-microsecond round trip, and picks the fabric by probe latency, not peak bandwidth. We instantiate the cost model and predicate for MLA, but neither is MLA-specific: they apply wherever compression or sparse selection shrinks attention to small chunks (DeepSeek-V3.2, V4, and GLM-5.1 today). Extending them to a new architecture requires measuring just two coefficients: the routed payload and fetch's move-the-cache cost.

Low-precision pretraining (FP8, MXFP4, NVFP4) is now standard for frontier language models, yet the literature is almost entirely achievability -- algorithms and empirical scaling laws -- with no matching characterization of what is information-theoretically possible. We study a B-bit quantized stochastic first-order oracle: an optimizer interacts for T rounds and receives, each round, a B-bit adaptive public-coin description of its stochastic gradient. Our main contribution is an exact reduction from optimizing a strongly convex quadratic family to interactively compressed Gaussian mean estimation -- under the B-bit oracle the query carries no information, so optimization collapses exactly onto a sequential distributed-estimation problem. This yields two unconditional lower bounds, a communication bound TB = Omega(d) and a statistical bound T = Omega(sigma^2 d / eps^2), and the sharp product-form bound T = Omega((sigma^2 d / eps^2) max{1, d/B}). The product form is also unconditional: a B-bit transcript carries at most O(TB / sigma^2) of Fisher trace about the mean, so bits rather than dimension limit the recoverable information, and combined with the multivariate van Trees inequality this gives the bound directly, without bounded-likelihood-ratio truncation. We give a near-matching achievability result with exact per-round bit accounting under a bounded-dynamic-range oracle, tight up to a logarithmic factor; the lower bound is for truly Gaussian (unbounded) gradients, and closing this oracle gap is left open. A sequential rate-distortion perspective extends the reduction to correlated and drifting oracles and corrects an earlier conjecture: positive noise correlation raises the bound by (1+rho)/(1-rho) rather than relaxing it. The bounds give an information-theoretic baseline for any low-bit gradient path, not an optimality claim about deployed FP4 systems.

Despite being ubiquitous in science, clustering remains a technique whose results are not quantitatively scrutinized via a framework. We present an analysis called evaluating replicability via iterative clustering assignments (ERICA) that is applied to a dataset to determine whether clusters are identified in a replicable manner. The pipeline computes a statistic that describes whether structure is found in a dataset. Quantitative visualization methods are presented to answer important questions such as the similarity between clusters, and the identity of points that may be outliers. When tested on synthetic data, the findings show clusters being discovered in a replicable manner. However, we note a possibility for non-replicable results when the pipeline is applied to three gene expression datasets for breast cancer subtype validation. The study underscores the need for rigorous inspection and offers a practical tool for doing so.

We study quantile regression in an extrapolation regime where the covariate takes unusually large values. Under regular variation assumptions, extreme observations can be effectively characterized through their angular components, enabling learning strategies that focus on the angle of the most extreme observations. This approach is formalized through the minimization of an asymptotic conditional risk that localizes learning in the tail of the covariate distribution. We propose a novel Support Vector Machine (SVM) framework for extreme quantile regression, leveraging reproducing kernel Hilbert spaces to handle high-dimensional and nonlinear settings. Our method also accommodates unbounded response variables and avoids restrictive transformations. We establish finite-sample learning guarantees under mild regularity assumptions. The proposed framework unifies ideas from statistical learning and multivariate extremes, providing a tractable and theoretically grounded approach to extrapolation. We complement our theoretical findings with an empirical study on river flow data from the Danube, demonstrating the practical relevance of our methods.

Recent advancements in multimodal large language models (MLLMs) have achieved remarkable progress in multimodal reasoning and code generation, catalyzing a new paradigm for front-end development. In particular, these models can directly transform visual designs into executable code, significantly improving the efficiency and adaptability of web development. Modern web applications are dynamic and interactive, featuring frequent user-page interactions. However, existing benchmarks largely evaluate the code generation of static webpages, ignoring the complex interactive behaviors in real-world applications. Besides, their evaluation criteria remain confined to visual fidelity and code structure, overlooking the interaction consistency between the generated and the reference webpages. To address these limitations, we introduce WebIGBench, the first benchmark designed to evaluate code generation for interactive webpages with complex interactions. By combining manually designed interaction paths with UI automation, we collected 103 complex webpages from real-world websites. This benchmark covers 5 popular interactive action types (e.g., click, input) involving 871 distinct interactive actions. Moreover, we propose a novel evaluation pipeline to address the gap in automated assessment of interactive actions. Extensive experiments on several representative MLLMs reveal the performance boundaries of current models in interactive webpage code generation using WebIGBench. The proposed benchmark is available at https://github.com/anoa12159-hue/WebIGBench_eval.

Training logistic regression over encrypted data has emerged as a prominent approach to addressing security concerns in recent years. In this paper, we introduce an efficient gradient variant, termed the \textit{quadratic gradient}, which is specifically designed for privacy-preserving logistic regression while remaining equally effective in plaintext optimization. By incorporating this quadratic gradient, we enhance Nesterov's Accelerated Gradient (NAG), Adaptive Gradient (AdaGrad), and Adam algorithms. We evaluate these enhanced algorithms across various datasets, with experimental results demonstrating state-of-the-art convergence rates that significantly outperform traditional first-order gradient methods. Furthermore, we apply the enhanced NAG method to implement homomorphic logistic regression training, achieving comparable performance within only four iterations. The proposed quadratic-gradient approach offers a unified framework that synergizes the advantages of first-order gradient methods and second-order Newton-type methods, suggesting broad applicability to diverse numerical optimization tasks.

Stochastic approximation (SA) is a method for finding the root of an operator perturbed by noise. The focus of this paper is studying the distribution of SA iterates in finite time. In general, it is not possible to characterize the exact distribution, and therefore our goal is to find an approximation which can yield useful tail bounds. Inspired by the rich literature on the asymptotic normality of rescaled SA iterates, we approximate the pre-limit distributions by a sequence of Gaussians whose covariance is recursively defined. In particular, we establish explicit bounds on the Wasserstein-1 distance between the rescaled iterate at time $k$ and the aforementioned Gaussian for various choices of step-sizes. Since these covariances converge to the classical asymptotic limit, our analysis also provides a convergence rate for asymptotic normality as a by-product. As an immediate consequence of our bounds, we obtain tail bounds on the error of SA iterates at any time. Finally, we establish the sharpness of our rates by providing matching lower bounds and validate our findings through simulations. We obtain the sharp rates by first studying the convergence rate of the discrete Ornstein-Uhlenbeck (O-U) process driven by general noise, whose stationary distribution is identical to the limiting Gaussian distribution of the rescaled SA iterates. We believe that this is of independent interest, given its connection to sampling literature. The analysis involves adapting Stein's method for Gaussian approximation to handle the matrix weighted sum of i.i.d. random variables. The desired finite-time bounds for SA are obtained by characterizing the error dynamics between the rescaled SA iterate and the discrete time O-U process and combining it with the convergence rate of the latter process.

With an evolutionary approach, the basis of morality can be explained as adaptations to problems of cooperation. With 'evolution' taken in a broad sense, AIs that satisfy the conditions for evolution to apply will be subject to the same cooperative evolutionary pressure as biological entities. Here the adaptiveness of increased cooperation as material safety and wealth increase is discussed -- for humans, for other societies, and for AIs. Diminishing beneficial returns from increased access to material resources also suggests the possibility that, on the whole, there will be no incentive to for instance colonize entire galaxies, thus providing a possible explanation of the Fermi paradox, wondering where everybody is. It is further argued that old societies could engender and eventually give way to super-AIs, since it is likely that super-AIs are feasible, and fitter. Closing is an aside on effective ways for morals and goals to affect life and society, emphasizing environments, cultures, and laws, and exemplified by how to eat. 'Diminishing returns' is defined, as less than roots, the inverse of infeasibility. It is also noted that there can be no exponential colonization or reproduction, for mathematical reasons, as each entity takes up a certain amount of space. Appended are an algorithm for colonizing for example a galaxy quickly, models of the evolution of cooperation and fairness under diminishing returns, and software for simulating signaling development.

Many modern applications involve predicting structured, non-Euclidean outputs such as probability distributions, networks, and symmetric positive-definite matrices. These outputs are naturally modeled as elements of general metric spaces, where classical regression techniques that rely on vector space structure no longer apply. We introduce E2M (End-to-End Metric regression), a deep learning framework for predicting metric space-valued outputs. E2M performs prediction via weighted Fréchet means over training outputs, where the weights are learned by a neural network conditioned on the input. This construction provides a principled mechanism for geometry-aware prediction that avoids surrogate embeddings and restrictive parametric assumptions, while fully preserving the intrinsic geometry of the output space. We establish theoretical guarantees, including a universal approximation theorem that characterizes the expressive capacity of the model and a convergence analysis of the entropy-regularized training objective. Through extensive simulations involving probability distributions, networks, and symmetric positive-definite matrices, we show that E2M consistently achieves state-of-the-art performance, with its advantages becoming more pronounced at larger sample sizes. Applications to human mortality distributions and New York City taxi networks further demonstrate the flexibility and practical utility of this framework.

In collaborative active learning, where multiple agents try to learn labels from a common hypothesis, we introduce an innovative framework for incentivized collaboration. Here, rational agents aim to obtain labels for their data sets while keeping label complexity at a minimum. We focus on designing (strict) individually rational (IR) collaboration protocols, ensuring that agents cannot reduce their expected label complexity by acting individually. We first show that given any optimal active learning algorithm, the collaboration protocol that runs the algorithm as is over the entire data is already IR. However, computing the optimal algorithm is NP-hard. We therefore provide collaboration protocols that achieve (strict) IR and are comparable with the best known tractable approximation algorithm in terms of label complexity.

Muscovite mica is a translucent, layered silicate mineral whose basal cleavage, low radiogenic background, gigayear exposures, and demonstrated track retention over geological timescales make it a compelling target for rare particle searches. In this work, we develop a new framework for detecting heavy composite dark matter using muscovite mica as a paleodetector. We model melt track formation by heavy composite dark matter transiting through mica using a Sedov-Taylor thermal spike formalism, and validate the sub-micron regime with SRIM/TRIM simulations of nuclear recoil cascades, which also calibrate the phonon efficiency governing local energy deposition. We demonstrate a novel readout method using rapid X-ray fluorescence mapping with a copper backing contrast technique, capable of identifying micron-scale damage features in cleaved mica sheets over macroscopic scan areas, and calibrate the minimum detectable track size using laser-ablated defect regions. We present projected sensitivities for opaque and diffuse composite dark matter, including a sub-melt hole-channel detection mode for large composites substantially attenuated by overburden. We also revisit prior dark matter exclusions from etched mica searches, identifying shortcomings that compromise the robustness of these constraints.

Multilayers of Babinet complementary periodic structures constructed with miniarrays of spherical plasmonic nanoresonators were optimized to ensure Generalized Faraday Rotation. Nonreciprocal rotation and asymmetric transmission were achieved in spectrally overlapping regions due to the reach physics involving (i) symmetry breaking via coupled localized modes, (ii) Brillouin zone-folding stemmed from constituent sub-lattices forming in-plane twisted coupled loops, (iii) interlayer coupling between Babinet complementary patterns. The nanophotonical phenomena include (i) quasi-BIC resonances, (ii) hierarchically coupled localized and propagating modes that results in time-periodic Floquet modulation, (iii) initialization of synthetic potentials tuneable independently via intra and inter-layer parameters. The unique bianisotropic composites result in a synthetic vector gauge and emulated magnetic field manifesting itself in tilted-precessing magnetic dipoles and the accompanying modulation being time-periodic, inherently ensures a synthetic dimension. The asymmetric transmission is enhanced in the classical sense along quantized flat bands, and in mixed and forward bases inside finite wavelength-and-tilting intervals overlapping with nonreciprocal polarization rotation. The transmitted pulse re-shaping proves beating of nearby resonant modes, the loss can be compensated with active ad-layers thereby resulting in Faraday isolator capability. The multilayers synthetize topological phenomena in high-dimensional synthetic parameter spaces.

We study stochastic completeness for landmark spaces equipped with Riemannian metrics induced by right-invariant metrics on subgroups of the diffeomorphism group of the shape domain. We extend a previous stochastic completeness result, which only covers the case of exactly two landmarks, to landmark spaces with any number of landmarks. This succeeds the characterization of geodesic completeness for landmark spaces with arbitrary numbers of landmarks, and thus finishes the completeness characterization for landmark spaces by covering the stochastic case. The proof makes use of Grigor'yan's volume growth criterion for stochastic completeness, which requires a suitable upper bound for the volume of growing geodesic balls. We obtain quantitative controls for geodesic balls in the landmark space by bounding both its Euclidean size and the rate at which pairwise landmark distances can approach zero. We then combine this with a lower bound on the minimal eigenvalue of the landmark cometric in terms of the Fourier transform of the kernel to yield volume growth bounds sufficient to prove stochastic completeness of landmark spaces for wide classes of kernels, including Matérn kernels.

We show that for any set of $n$ unit vectors $v_1,\ldots,v_n$ in a real Hilbert space and positive numbers $p_1,\ldots,p_n$ satisfying $\sum_j p_j = 1$, there exists a unit vector $u$ such that \[ \sum_{j=1}^n \frac{p_j^2}{\langle v_j, u\rangle^2}\leq 1. \] This inequality is a weighted version of the strong polarization inequality. As immediate corollaries, it yields a polarization inequality for products of powers of linear functionals and a strengthening of Bang's classical plank theorem for Hilbert spaces. The proof follows the approach introduced by Martínez and Ortega-Moreno in their recent solution to the strong polarization conjecture posed by Ball and Frenkel. We further note that our weighted inequality admits a Shannon-entropy interpretation: in a random sensing model, the entropy of the weights controls the minimum expected logarithmic loss.

Self-Interacting Dark Matter (SIDM) models with large cross sections at relative velocities below $\sim100\,{\rm km \, s}^{-1}$ can be tested with dwarf galaxy observations. We analyze six dark-matter-only zoom-in $\sim10^{10}\,{\rm M}_\odot$ halos with diverse assembly histories, adopting a cross section over mass of $σ/m = 70\,cm^2 \, g^{-1}$. We find that mergers inject orbital kinetic energy into the halo, altering the heat transport and the gravothermal evolution of the core. Three of the six halos -- those with the most quiescent merger histories -- show clear signs of core collapse in these simulations. Halos with sustained mergers do not collapse. Furthermore, merger-induced heat transport drives two non-collapsing halos to central densities well below the predictions of the gravothermal fluid model. These findings suggest a novel mechanism for producing dark-matter-deficient galaxies and expanding the diversity of rotation curves beyond what halo concentration alone predicts. Merger histories are thus essential for understanding central density distributions of dwarf galaxy halos in SIDM.

We study pure unital completely positive maps on the finite Toeplitz operator system $ T_{d}$ of $d \times d$ Toeplitz matrices. Our first main result gives an explicit characterization of pure UCP maps from $T_{d}$ to $M_n$ in terms of positive $n\times n$ matrix-valued trigonometric polynomials of degree at most $d-1$. This characterization provides a checkable criterion for deciding when a given UCP map is pure. As a first application, we show that every pure UCP map from $ T_{d}$ to $M_n$ admits a unique UCP extension to the generated $C^*$-algebra. As a second application, we prove that, for each fixed $n$, the space of pure UCP maps from $T_{d}$ to $M_n$, equipped with the matricial Connes distance, converges in the Gromov--Hausdorff sense to the space of normalized positive $n\times n$ matrix-valued Borel measures on the unit circle, equipped with the matricial Monge--Kantorovich distance.

Subwavelength atomic tweezer arrays, in which atoms can be positioned at distances smaller than their emission wavelength, have been proposed as a versatile platform to study collective emission phenomena, such as superradiance and subradiance. Experimentally, the realization of such arrays has been a challenge as typical emission wavelengths in the visible or near-infrared are short compared to typical tweezer spacings in the micrometer range. Here, we use $^{88}$Sr atoms in optical tweezer arrays to access a mid-infrared transition at 2,923 nm ($5s5p\:^{3}P_{2} \rightarrow\, 5s4d\:^{3}D_{3}$). We identify a magic trapping wavelength at 597.14(3) nm and demonstrate single-atom preparation and imaging with high fidelity. In addition, using 2,923 nm light, we demonstrate resolved-sideband cooling of tweezer-trapped strontium. Beyond enabling studies of collective emission phenomena in flexible arrangements of atoms, our platform opens novel opportunities for dipolar many-body physics and enhanced control over Rydberg dynamics and the strontium fine-structure qubit.

We show solubility of the conjugacy problem for Dehn twist automorphisms of finitely generated free products of free abelian groups.

Muon tomography based on multiple Coulomb scattering provides a non-destructive method to image dense and shielded objects using naturally occurring cosmic-ray muons. In the context of nuclear waste characterization, we present the experimental imaging of a 205-L mock waste barrel using a dedicated 1m$^2$ muon scattering tomography test bench. The system employs multiplexed resistive Micromegas detectors, enabling stable and high-precision muon tracking. Monte Carlo simulations are first used to characterize material-dependent scattering signatures and to quantitatively assess identification performance using statistical reconstruction. These simulation-based results are then used to define objective discrimination thresholds, which are subsequently applied to experimental data for the localization and identification of internal anomalies. Using an Angle Statistics Reconstruction algorithm, we achieve a spatial resolution of 10 mm and demonstrate the three-dimensional imaging of an internal structure containing both low- and high-radiation length materials. Material discrimination performance is evaluated using receiver operating characteristic analysis, yielding high identification efficiency for dense metallic inclusions such as lead and steel (AUC $\geq$ 0.96) within acquisition times of a few days, while cavities also exhibit strong contrast. Experimental results show good agreement with detailed Monte Carlo simulations. By establishing a continuous workflow from simulation-based performance characterization to practical application on measured data, this work provides a quantitatively validated framework for muon scattering tomography applied to complex, shielded objects.

Irregular dust aggregates immersed in plasma sheaths experience several orientation-dependent torques that can modify their rotational dynamics and stability. Here, we investigate the rotational dynamics of charged irregular aggregates under conditions representative of a GEC rf plasma cell using self-consistent numerical simulations. The aggregates rotate freely in a unidirectional sheath electric field that drives an ion flow, allowing the torque contributions acting on the aggregate to be evaluated throughout the motion. The results show that the sheath electric field is the main driver of rotation and aligns the aggregate electric dipole moment with the sheath field direction. The ion wake modifies this alignment: its axial field component produces an opposing torque, while its transverse components introduce a destabilizing contribution that leads to small oscillations about the equilibrium orientation. The rotational equilibrium is described by an interaction energy well whose spring constant and depth increase with the sheath electric field magnitude, indicating stronger alignment and greater resilience to angular perturbations at higher fields. A second order multipole expansion of the aggregate ion interaction shows that the dipolar term governs the ion contribution to the aligning torque, supporting a dipole ion approximation across the examined conditions. These results identify the sheath electric field as the principal stabilizing mechanism for irregular aggregate rotation and clarify how ion wake fields perturb the equilibrium orientation.

A fundamental goal in climate attribution is to estimate how forced climate change contributes to observed extreme weather events. The storyline attribution method compares an observed weather event, conditional on its atmospheric dynamic state (i.e., atmospheric circulation), in the current, 'factual' climate to an event with very similar circulation conditions in a hypothetical, 'counterfactual' climate. However, physical climate models cannot directly transfer these storyline counterfactuals across different climate forcing states. Statistical and machine learning techniques may overcome this limitation; yet, emulating circulation-conditional extreme events under different climate states is challenging. Here, we demonstrate distributional autoencoders (DAEs) as a versatile method for generating climate counterfactuals. They model the full distribution of spatially resolved European temperature fields conditional on the atmospheric circulation state and the mean global warming level. These distributions allow for deriving meaningful conditional probability ratios, which is a particular advantage of the DAE-based storyline approach. We train DAEs on fully coupled climate model simulations and we evaluate the modelled distributions across different factual and storyline-based counterfactual climate model simulations. In an illustrative case study, we revisit the 2003 European heatwave and we generate counterfactuals for a hypothetical `2003-like European heatwave' using ERA5 circulation, which we hypothesize to occur a quarter century (2028) and a half century (2053) after 2003. The conditional intensity would increase from 29.3 °C in 2003, to 30.3 °C and 32.1 °C in 2028 and 2053, respectively and conditional probability ratios would be 2.1 and 3.2 when compared to 2003.

A diagrammatic Monte Carlo evaluation of the ladder series contributions to the correlation potential (self energy) of a positron in the field of a molecule is presented. The $GW$@TDHF, virtual-positronium ($T$-matrix), and positron-hole Goldstone ladder series contributions are stochastically sampled order-by-order within the Tamm-Dancoff approximation, which is exact for the latter two classes, with Ces{á}ro-Riesz resummation used to extrapolate to infinite order. Gaussian bases are employed and Coulomb matrix elements are represented via density fitting, with the three centre integrals the largest arrays required to be stored in memory. The stochastic approach thus realizes a reduction in memory of the largest arrays required on the order of the number of molecular orbitals in the basis $N\sim$10$^2$--10$^3$ compared to the exact deterministic solution of Bethe-Salpeter equations [J. Hofierka, B. Cunningham, C. M. Rawlins, C. H. Patterson and D. G. Green, Nature {\bf 606}, {688} (2022)]. Benchmark results for lithium hydride show quantitative agreement with exact diagonalisation, notably demonstrating the successful stochastic summation of the virtual-positronium infinite electron-positron ladder series.

Recent leaderboard-based evaluations of large language models aggregate user feedback by fitting a Bradley--Terry model to pairwise comparisons, producing a single global ranking based on a latent quality score. While appealing for its simplicity, this approach is incompatible with heterogeneous preferences: when LLMs are used across diverse tasks and use cases, users who favor fundamentally different model behaviors can be systematically misrepresented when collapsed into a single quality score. To address this issue, we study \emph{pluralistic leaderboards} that aim to remain \emph{stable} with respect to heterogeneous user populations. Drawing on ideas from social choice theory, we adapt the notion of \emph{local stability}, which requires that no model outside the top-$k$ positions is collectively preferred to the top-$k$ set by more than $O(1/k)$ fraction of users. Building on techniques from the social choice literature, we design an alternative leaderboard mechanism that satisfies local stability while eliciting only $\widetilde{O}(k)$ pairwise comparisons per user, where $k$ is the size of the prefix for which stability is guaranteed. Using data from LMArena, we show that standard Bradley--Terry aggregation can violate local stability in practice, whereas our method provides substantially stronger stability guarantees.