We study the neutral massive Maxwell (Proca) equation on subextremal Reissner--Nordström exteriors. After spherical-harmonic decomposition, the odd sector is scalar, while the even sector remains a genuinely coupled $2\times2$ system. Our starting point is that this even system admits an exact asymptotic polarization splitting at spatial infinity. The three resulting channels carry effective angular momenta $\ell-1$, $\ell$, and $\ell+1$, and these are precisely the indices that govern the late-time thresholds. % For each fixed angular momentum we develop a threshold spectral theory for the cut-off resolvent. We prove meromorphic continuation across the massive branch cut, rule out upper-half-plane modes and threshold resonances, and obtain explicit small- and large-Coulomb expansions for the branch-cut jump. Inverting this jump yields polarization-resolved intermediate tails together with the universal very-late $t^{-5/6}$ branch-cut law. % At the full-field level, high-order angular regularity allows us to sum the modewise leading terms on compact radial sets and obtain a two-regime asymptotic expansion for the radiative branch-cut component of the Proca field, with explicit coef
There have recently been many efforts to create machine learnt atmospheric emulators designed to replace physical models. So far these have mainly focused on medium-range weather forecasting, where these `Machine Learnt Weather Prediction' (MLWP) models can outperform leading operational forecasting centres. However, because of this focus on shorter timescales, many of these emulators ignore the effects of the ocean, and take no ocean variables as inputs. We hypothesise that such MLWP models have learnt a best-guess of the evolution of the atmosphere, by implicitly inferring ocean conditions from atmospheric states, with no access to ocean data. Turning this limitation into a strength, we use it as a means to study the role of the oceans on the evolution of the atmosphere. By exploring how model forecast errors relate to properties of the air-sea interface, we infer what ocean information these atmospheric emulators are able to derive from atmospheric data alone, and what they cannot. This highlights the regions and processes through which the ocean independently influences the atmosphere on fast timescales. We perform this analysis for GraphCast, finding clear relationships betwee
Meaningful scores for forecast verification are essential for developing reliable forecasts, and there has been much effort to develop scores that align well with human perceptions of forecast quality. Whilst many of these scores have intuitive interpretations, relatively little is known about how these scores rank different forecasts, and how scores reflect forecast error. We theoretically explore the behaviour of two scores that fall within the `neighbourhood' paradigm of spatial verification; the Fractions Skill Score (FSS) and Brier Divergence Skill Score (BDnSS). We investigate how each score ranks forecasts with two types of error; errors in the mean frequency (corresponding to intensity or shape errors) and errors in the standard deviation (corresponding to errors in spatial structure, such as blurring or excess noise). We find that under many situations the FSS assigns higher scores to forecasts that over-predict mean frequency, thus theoretically confirming the need to use the FSS with percentile thresholds. Both scores assign higher scores to smoother forecasts in many situations, a reflection of the `double penalty' problem; however, we observe that size of this effect i
We prove a threshold-sharp stability theory for the conformal scalar-curvature sector on zero-curvature Carter backgrounds. The main result is a fully closed bounded-slab theorem: the reflecting evolution is constructed, the conserved energy is proved positive, the complete affine threshold obstruction is identified, and all remaining finite-energy dynamics are shown to be uniformly stable with no unstable modes. This is the sharp statement for compact reflecting slabs, where genuine time decay is false in general. We then extend the same threshold philosophy to black-hole exteriors, separating the intrinsic conformal mechanism from the exterior scalar-wave inputs needed for red-shift, local energy, limiting absorption, and zero-frequency control. The framework gives main applications to Kerr, Reissner-Nordström, slowly rotating weakly charged Kerr-Newman wall exteriors, and extremal horizon-charge obstructions. Our precise result is that it proves stability only for the conformal scalar-curvature sector, not tensorial or nonlinear gravitational stability, and it distinguishes boundedness, qualitative local decay, polynomial decay, and extremal Aretakis-type obstruction without con
Repository-level coding benchmarks face a trade-off between task difficulty and evaluation reliability: tasks that challenge frontier models often involve large codebases with incomplete test coverage, while human review does not scale. We introduce TensorBench, a benchmark of 199 feature-addition and refactoring tasks on an open-source compiler-based tensor framework that extends PyTorch with first-class support for dense and sparse tensors. Tasks cover new sparse formats, dense optimization passes, IR transformations, scheduler changes, runtime components, and high-level numerical operators. TensorBench grades each run by applying the agent's patch and running the framework's test suite, which includes the pre-existing randomized regression tests and any tests the agent adds. For feature-addition tasks, a pass means that the patched repository preserves the tested pre-existing behavior and satisfies the agent-added checks for the requested feature. We evaluate seven coding agents spanning three frontier model families and one open-weight model. Pass rates under this criterion range from $64.8\%$ for the strongest agent to $22.1\%$ for the weakest. Agents pass different subsets of
Understanding how fast atmospheric variability shapes slow climate variability and sensitivity remains a central challenge in Earth-system science. Recent advances in machine-learned (ML) atmospheric models have demonstrated remarkable skill on weather timescales, but their emergent behaviour in a fully coupled climate system remains largely unexplored. We present early results from a new hybrid modelling framework, in which the ACE2 ML atmospheric emulator is interactively coupled to the NEMO ocean model. We report on a set of 70-year coupled simulations (1950-2020 historical forcing and fixed-1950s control). These experiments represent, to our knowledge, the first multi-decadal integrations of a machine-learned atmosphere interacting with a full-depth dynamical ocean. Several historical and fixed-1950s control simulations from the fully dynamic global coupled climate model EC-Earth, which has the same ocean component used in ACE2-NEMO, are also considered for comparison. We assess the behaviour of the coupled system, with particular focus on low-frequency tropical variability and the climate response to greenhouse-gas forcing. Analysis of potentially emergent El Niño-like variabi
Spin waves (magnons) in 2D materials have received increasing interest due to their unique states and potential for tunability. However, many interesting features of these systems, including Dirac points and topological states, occur at high frequencies, where experimental probes are limited. Here, we study a crystal formed by patterning a hexagonal array of holes in a perpendicularly magnetized thin film. Through simulation, we find that the magnonic band structure imitates that of graphene, but additionally has some kagome-like character and includes a few flat bands. Surprisingly, its nature can be understood using a 9-band tight-binding Hamiltonian. This clear analogy to 2D materials enables band-gap engineering in 2D, topological magnons along 1D phase boundaries, and spectrally isolated modes at 0D point defects. Interestingly, the 1D phase boundaries allow access to the valley degree of freedom through a magnonic analog of the quantum valley-Hall insulator. These approaches can be extended to other magnonic systems, but are potentially more general due to the simplicity of the model, which resembles existing results from electron, phonon, photon, and cold atom systems. This
The European Union aims to achieve climate-neutrality by 2050, with interim 2030 targets including 55% greenhouse gas emissions reduction compared to 1990 levels, 10 Mt p.a. of a domestic green H2 production, and 50 Mt p.a. of domestic CO2 injection capacity. To support these targets, Projects of Common and Mutual Interest (PCI-PMI) - large infrastructure projects for electricity, hydrogen and CO2 transport, and storage - have been identified by the European Commission. This study focuses on PCI-PMI projects related to hydrogen and carbon value chains, assessing their long-term system value and the impact of pipeline delays and shifting policy targets using the sector-coupled energy system model PyPSA-Eur. Our study shows that PCI-PMI projects enable a more cost-effective transition to a net-zero energy system compared to scenarios without any pipeline expansion. Hydrogen pipelines help distribute affordable green hydrogen from renewable-rich regions in the north and southwest to high-demand areas in central Europe, while CO2 pipelines link major industrial emitters with offshore storage sites. Although these projects are not essential in 2030, they begin to significantly reduce an
We prove that, for every polyhedral or $C^1$ norm on $\mathbb{R}^d$ and every set $E \subseteq \mathbb{R}^d$ of packing dimension $s$, the packing dimension of the distance set of $E$ with respect to that norm is at least $\tfrac{s}{d}$. One of the main tools is a nonlinear projection theorem extending a result of M. Järvenpää. An explicit construction follows, demonstrating that these distance sets bounds are sharp for a large class of polyhedral norms.
Aminoacetonitrile occupies a prime importance in the interface between astrochemistry and prebiotic chemistry. Its detection in the ISM establishes it as part of the organic inventory of star-forming regions, while its role as a glycine precursor highlights its significance for origins-of-life scenarios. In this work, electron scattering from aminoacetonitrile has been studied using the $R$-matrix method in the low-energy range from $\sim$0 to 10 eV. The calculations were carried out within the $C_{s}$ point group using static-exchange (SE), static-exchange plus polarisation (SEP), and configuration interaction (CI) models, with two basis sets (6-311G* and cc-pVTZ) to understand their dependence on cross section. Various scattering observables, such as differential elastic cross section, integral elastic, excitation, and momentum transfer cross sections, were examined. Since aminoacetonitrile is a prebiotically relevant molecule, these findings provide valuable insight into electron-driven processes in complex organic systems and form a theoretical foundation for future work on electron-induced reactivity in prebiotic and astrophysical environments.
LLMs are increasingly pervasive in the security environment, with limited measures of their effectiveness, which limits trust and usefulness to security practitioners. Here, we present an open-source evaluation framework and benchmark metrics for evaluating LLM-generated cybersecurity rules. The benchmark employs a holdout set-based methodology to measure the effectiveness of LLM-generated security rules in comparison to a human-generated corpus of rules. It provides three key metrics inspired by the way experts evaluate security rules, offering a realistic, multifaceted evaluation of the effectiveness of an LLM-based security rule generator. This methodology is illustrated using rules from Sublime Security's detection team and those written by Sublime Security's Automated Detection Engineer (ADE), with a thorough analysis of ADE's skills presented in the results section.
Ethylene glycol is a prebiotically relevant complex organic molecule detected in interstellar and cometary environments, yet quantitative low-energy electron-ethylene glycol scattering data remain limited for astrochemical modeling. This work presents an R-matrix study of low-energy electron collisions with ethylene glycol over the 0 to 12 eV energy range, using static exchange (SE), static exchange plus polarization (SEP), and configuration interaction (CI) models with 6-311G* and cc-pVTZ basis sets. We compute elastic, excitation, and differential cross sections within a close coupling framework. The dataset offers benchmark inputs for astrochemical models, supporting interpretation of ethylene glycol abundances in space and refining constraints on electron-induced prebiotic pathways.
Machine-learnt weather prediction (MLWP) models are now well established as being competitive with conventional numerical weather prediction (NWP) models in the medium range. However, there is still much uncertainty as to how this performance extends to longer timescales, where interactions with slower components of the earth system become important. We take GenCast, a state-of-the-art probabilistic MLWP model, and apply it to the task of seasonal forecasting with prescribed sea surface temperature (SST), by providing anomalies persisted over climatology (GenCast-Persisted) or forcing with observations (GenCast-Forced). The forecasts are compared to the European Centre for Medium-Range Weather Forecasts seasonal forecasting system, SEAS5. Our results indicate that, despite being trained at short timescales, GenCast-Persisted produces much of the correct precipitation patterns in response to El Niño and La Niña events, with several erroneous patterns in GenCast-Persisted corrected with GenCast-Forced. The uncertainty in precipitation response, as represented by the ensemble, compares favourably to SEAS5. Whilst SEAS5 achieves superior skill in the tropics for 2-metre temperature and
The higher-order autocorrelations of integer-valued or rational-valued gridded data sets appear naturally in X-ray crystallography, and have applications in computer vision systems, correlation tomography, correlation spectroscopy, and pattern recognition. In this paper, we consider the problem of reconstructing a gridded data set from its higher-order autocorrelations. We describe an explicit reconstruction algorithm, and prove that the autocorrelations up to order 3r + 3 are always sufficient to determine the data up to translation, where r is the dimension of the grid. We also provide examples of rational-valued gridded data sets which are not determined by their autocorrelations up to order 3r + 2.
Exploration is a key part of many video games. We investigate the using an exploratory agent to provide feedback on the design of procedurally generated game levels, 5 engaging levels and 5 unengaging levels. We expand upon a framework introduced in previous research which models motivations for exploration and introduce a fitness function for evaluating an environment's potential for exploration. Our study showed that our exploratory agent can clearly distinguish between engaging and unengaging levels. The findings suggest that our agent has the potential to serve as an effective tool for assessing procedurally generated levels, in terms of exploration. This work contributes to the growing field of AI-driven game design by offering new insights into how game environments can be evaluated and optimised for player exploration.
The rapid growth in the size of deep learning models strains the capabilities of traditional dense computation paradigms. Leveraging sparse computation has become increasingly popular for training and deploying large-scale models, but existing deep learning frameworks lack extensive support for sparse operations. To bridge this gap, we introduce Scorch, a library that seamlessly integrates efficient sparse tensor computation into the PyTorch ecosystem, with an initial focus on inference workloads on CPUs. Scorch provides a flexible and intuitive interface for sparse tensors, supporting diverse sparse data structures. Scorch introduces a compiler stack that automates key optimizations, including automatic loop ordering, tiling, and format inference. Combined with a runtime that adapts its execution to both dense and sparse data, Scorch delivers substantial speedups over hand-written PyTorch Sparse (torch.sparse) operations without sacrificing usability. More importantly, Scorch enables efficient computation of complex sparse operations that lack hand-optimized PyTorch implementations. This flexibility is crucial for exploring novel sparse architectures. We demonstrate Scorch's ease
In healthcare, medical image segmentation is crucial for accurate disease diagnosis and the development of effective treatment strategies. Early detection can significantly aid in managing diseases and potentially prevent their progression. Machine learning, particularly deep convolutional neural networks, has emerged as a promising approach to addressing segmentation challenges. Traditional methods like U-Net use encoding blocks for local representation modeling and decoding blocks to uncover semantic relationships. However, these models often struggle with multi-scale objects exhibiting significant variations in texture and shape, and they frequently fail to capture long-range dependencies in the input data. Transformers designed for sequence-to-sequence predictions have been proposed as alternatives, utilizing global self-attention mechanisms. Yet, they can sometimes lack precise localization due to insufficient granular details. To overcome these limitations, we introduce TransDAE: a novel approach that reimagines the self-attention mechanism to include both spatial and channel-wise associations across the entire feature space, while maintaining computational efficiency. Additi
Carbon dioxide levels below the soil surface are an important measurement relating to plant health, especially for plants such as perennial grasses in northern climates where ice encasement can occur over winter. In such cases, the CO$_2$ levels can build up and become toxic. This is likely a significant contributor to turfgrass death over winter; however, there is an insufficient amount of data regarding this phenomenon in large part due to the lack of effective sensors. Many off the shelf CO$_2$ sensors exist, but they are not sufficiently hardened for in ground deployment over winter. As a result, the only options currently available are very costly automated gas samplers or manual sampling at intervals with laboratory testing -- a process that results in a limited number of data points and is labor intensive. To combat this problem we have taken an established NDIR CO$_2$ sensor and hardened it for use in winter and ice encased environments to allow for continuous automated sampling of subsurface CO$_2$ levels to better understand ice encasement damage in perennial grass systems.
Outlier Features (OFs) are neurons whose activation magnitudes significantly exceed the average over a neural network's (NN) width. They are well known to emerge during standard transformer training and have the undesirable effect of hindering quantisation in afflicted models. Despite their practical importance, little is known behind why OFs emerge during training, nor how one can minimise them. Our work focuses on the above questions, first identifying several quantitative metrics, such as the kurtosis over neuron activation norms, to measure OFs. With these metrics, we study how architectural and optimisation choices influence OFs, and provide practical insights to minimise OFs during training. As highlights, we introduce a novel unnormalised transformer block, the Outlier Protected block, and present a previously unknown benefit of non-diagonal preconditioning optimisers, finding both approaches to significantly reduce OFs and improve quantisation without compromising convergence speed, at scales of up to 7B parameters. Notably, our combination of OP block and non-diagonal preconditioner (SOAP) achieves 14.87 int8 weight-and-activation perplexity (from 14.71 in standard precisi