Papers

Probabilistic Graphical Models (PGMs), especially Bayesian Networks (BNs), expose directed structure and probabilistic parameters, making them natural symbolic targets for neurosymbolic AI. Yet training text-to-parameterized-BN systems requires paired text-to-BN resources unavailable at scale. We introduce PRISM-BN, a controlled corpus of 5054 BN-grounded descriptions paired with discrete reference BNs containing variables, states, directed edges, root priors, and full multi-parent CPDs across five domains. The instances are derived from 50 Wikipedia-seeded backbones, and their probabilities are internally constructed benchmark targets rather than externally validated causal estimates. PRISM-BN is built with PRISM, a marginal-first pipeline that elicits marginal and local joint distributions, analytically recovers normalized CPDs, and constructs locally reparameterized subgraphs. We define a benchmark with semantic node and state alignment, conditional structural scoring, and strict full-CPD evaluation. Across six LLM extractors, Node F1 ranges from 0.56 to 0.83, conditional Edge F1 from 0.90 to 0.97, and CPD-KL from 1.11 to 3.14. Conditional state and edge recovery remain consistently strong, whereas strict full-CPD agreement remains challenging. These trends persist with independently generated GPT-5.5 references, and a human pilot corroborates structural recoverability and similar probabilistic interpretations. PRISM-BN supports separate evaluation of structural recovery and probabilistic parameter estimation.

Large language models (LLMs) achieve strong performance but suffer from slow and costly inference. Existing acceleration methods often lead to noticeable performance degradation, while Mixture-of-Experts (MoE) models require extensive computational resources. In this paper, we propose L0-MoE, a lightweight MoE approach using L0-regularization to accelerate dense LLMs nearly without performance loss. Our method introduces a cluster confusion matrix for domain-aware dataset curation and applies dynamic batching for efficient training. Experiments show that L0-MoE achieves up to 2.5x speedup over dense models while maintaining competitive performance, outperforming existing LLM acceleration baselines.

The response of magnetic nanoparticles (MNPs) to applied magnetic fields underpins a broad range of biomedical and technological applications. In this Perspective, we review the principal modeling approaches for describing MNP dynamics across different physical regimes, ranging from coarse-grained macrospin descriptions to spatially resolved micromagnetic simulations. Selecting an appropriate model depends on the relevant energy scales and timescales, including those associated with magnetic anisotropy. We compare the assumptions, computational requirements, and regimes of applicability of the fixed-point-dipole, effective-field, thermal Stoner-Wohlfarth, diffusion-jump, coupled Landau-Lifshitz-Gilbert, egg, and micromagnetic models. Particular attention is given to coupling magnetization dynamics with translational and rotational particle motion, hydrodynamic interactions, and long-range dipolar interactions. By relating the relevant physical regimes to the resolution and computational cost of each approach, we provide practical guidance for model selection and outline challenges for predictive multiscale simulations of interacting MNP systems.

In this paper, we develop a polyhedral version of Milman's centro-affine spectral framework for full-dimensional origin-symmetric polytopes. A weighted graph Laplacian on the facets plays the role of the smooth centro-affine Laplacian. For $n\geq 3$, we prove that its first nonconstant even eigenvalue satisfies \[ \lambda_{1,e}(P)\geq n-1+\frac{1}{n-1} \] whenever $P$ is a local minimizer of $\lambda_{1,e}$ among origin-symmetric polytopes with the same facet normals, but not necessarily the same normal fan.

Single free-layer Magnetic Tunnel Junctions (MTJs) with a perpendicular easy axis driven by spin currents have demonstrated fast, deterministic switching, non-volatility, and low-power memory capabilities when integrated with modern nanoelectronic devices. In this article, we numerically investigate sub-ns and field-free switching characteristics of a p-MTJ with a Synthetic Antiferromagnet (SAF) based free layer structure using sequential sub-ns current pulses of Spin Orbit Torque (SOT) and Spin Transfer Torque (STT). While the SOT pulse applied to one layer decreases the transition time by bringing the coupled layers into an in-plane configuration, the subsequent STT pulse on the system determines the switching direction. Various pulse protocols have been investigated for both SOT and STT current amplitude and pulse widths, while also considering the effect of the Reference Layer (RL). While significant regions of deterministic switching events are observed, limitations in SOT, STT parameters are further investigated in presence of thermal fluctuations.

The main purpose of this paper is to introduce and study restricted Lie color triple systems. We consider first restricted Lie color algebras and then provide a definition and relevant properties of restricted Lie color triple systems. Moreover, we introduce and discuss representations of restricted Lie color algebras and restricted Lie color triple systems.

Software is a first-class scientific object, yet validated links between source code and the scholarly record remain largely absent from the Linked Open Data (LOD) cloud, isolating archived artefacts from semantic discovery. This paper presents an end-to-end reconciliation pipeline that harvests, validates, and models publication-to-repository pairs from sources where the link between a paper and its source code is explicit and editorially verified: the software-centric journals JOSS, SoftwareX, and IPOL, together with the reproducibility reports of the SIGMOD Availability and Reproducibility Initiative (ARI). This yields a curated corpus of 4,397 $\langle$DOI, repository-URL$\rangle$ pairs. We design two distinct application profiles grounded in Wikidata classes (one for scholarly articles, one for software instances) aligned with the schema.org and CodeMeta vocabularies. This architectural separation enables rule-based reconciliation at two granularities: lightweight, inline publication references or standalone, first-class Wikidata software nodes equipped with SWHIDs, Software Heritage's content-addressed identifiers. A read-only lookup against Wikidata shows that only 82 of the harvested repositories were already modelled there; human-reviewed batches have since created 4{,}182 new software items cross-linked to their articles. We further show that payloads of the emerging COAR Notify protocol, an external effort we do not develop, map natively onto our input format, so the same backend could later serve a live enrichment stream. Our core contribution is a pair of application profiles that turn Wikidata into a connector between the scholarly record and archived source code; we openly release all code, application profiles, and harvested datasets.

The success of Large Audio Language Models has driven the development of massive multimodal networks exceeding billions of parameters. However, the demand for privacy-preserving, low-latency processing has shifted focus toward Small Audio Language Models (SALMs) capable of on-device execution. In this paper, we introduce Samsone, a family of SALMs designed for edge computing. Our core model, Samsone-134M, establishes a new state-of-the-art for its size class across multiple benchmarks. We further explore the scaling laws of SALMs by introducing Samsone-99M and Samsone-356M. Despite their compact footprint, the Samsone family delivers performance competitive with models orders of magnitude larger. To foster open research and reproducibility, we train Samsone on publicly available data. We release the training code, model weights, mobile-optimized checkpoints and provide an open-source Android application to demonstrate real-time on-device inference of Samsone.

The orbital character of the so-called $A$-pocket in infinite-layer nickelates remains under debate. We investigate bulk NdNiO$_2$ using density-functional theory combined with dynamical mean-field theory and identify the $A$-pocket as a strongly hybridized state with substantial interstitial-$s$, Nd-$d_{xy}$ and Ni-d_${xz/yz}$ contributions. Our angle-resolved photoemission spectroscopy simulations reproduce the main polarization-dependent features measured experimentally. Removing the interstitial-$s$ matrix element leads to a clear disagreement with the measured Fermi surface maps, even though the interstitial-$s$ contribution is not dominant. Suppressing instead the Nd-d$_{xy}$ or Ni-$_{dxz/yz}$ matrix elements leaves the maps almost unchanged, because these are small at the zone corner. More generally, our results demonstrate that assigning the microscopic origin of spectral features in infinite-layer nickelates requires treating orbital hybridizations and photoemission matrix elements together.

Clustering is a fundamental task in data analysis, typically addressed through centroid-based methods such as K-means. In this work, we present a general framework for multi-domain clustering via measure quantization: given samples from multiple domains, we learn a shared set of cluster prototypes by minimizing a probability metric, such as the Sinkhorn divergence or the Maximum Mean Discrepancy, between each domain's probability measure and the measure of prototypes. Data points are then assigned to clusters either via nearest centroid, or via optimal transport, a collaborative strategy that couples all samples within a domain. A mini-batch optimization strategy makes both fitting and assignment scalable, reducing memory and computational cost while preserving clustering performance. Experimental results on 5 multi-domain benchmarks spanning image, audio and sensor data show that our Sinkhorn-based method consistently outperforms classical and multi-domain clustering baselines, and that this advantage persists when scaling to hundreds of thousands of samples.

Word Error Rate (WER), the most commonly used metric for Automatic Speech Recognition (ASR), treats every lexical deviation from the reference as equally costly, regardless of whether it changes meaning. This raises the question: does WER actually track how humans judge ASR transcript quality? We introduce HATS-en, an English dataset for human-centered ASR evaluation. Using this dataset, we benchmark lexical metrics against several configurations of BERTScore and SemDist, varying the language model, layer, and pooling strategy. We find that WER agrees least with human judgment among all metrics tested, that the best-performing SemDist configurations achieve the highest overall agreement, ahead of CER and BERTScore, and that no single model is best across settings. CER, despite its simplicity and low cost, remains remarkably close to these best configurations. In line with prior recommendations, our results support shifting ASR evaluation toward CER both for English and for morphosyllabic writing systems as it is a more interpretable and low-cost metric for what evaluation should actually capture, and using SemDist as a complementary evaluation.

Activation steering has become a widely used approach for controlling language models during explicit chain-of-thought (CoT) reasoning, motivating its extension to latent CoT. However, we find that steering continuous thoughts produces substantially weaker effects on subsequent language generation than steering explicit CoT, even when the hidden representations are moved by comparable amounts. We first show that task information remains identifiable in continuous thoughts. Hence, we hypothesize a latent-to-language transition gap, in which an intervention effect in latent space fails to transfer to language generation. Two further results support this hypothesis: the output distribution changes abruptly at the transition boundary, and task-related directions exert much weaker bidirectional control in latent CoT than in explicit CoT. These findings identify the transition interface as a central target for evaluating and designing future latent-steering methods.

Strong gravitational lenses are invaluable tools for addressing fundamental questions in astrophysics, from the nature of dark matter to the expansion of the universe. While current sky surveys have successfully identified thousands of lens candidates, the search methods employed face a critical challenge. The conventional approach relies on a "crop-and-classify" strategy, where small images are first cut out around billions of potential host galaxies before being individually classified. This process creates a significant computational and storage bottleneck that is unsustainable for future large-scale surveys. To overcome this limitation, we propose LenNet, an object detection model that identifies lenses directly within large, original survey images. Our method completely bypasses the inefficient cropping step by framing the problem as a direct detection and localization task. We initially train LenNet on simulated data to learn the complex features of gravitational lenses and then use transfer learning to fine-tune the model on a limited set of real, labeled examples from the Kilo-Degree Survey (KiDS). Our experiments show that LenNet performs remarkably well on real survey data, validating its potential as a highly efficient and scalable solution for lens discovery in massive astronomical surveys.

*Context.* Many lensing images are often obscured by foreground light from the central galaxies, making them challenging to detect. *Aims.* To address the limitations of previous lens search efforts, particularly for samples with smaller $R_E$ or faint lensed images, we developed a composite convolutional neural network framework that utilizes both U-Net and ResNet architectures for feature extraction and classification. *Methods.* We propose a hybrid search method that combines U-Net and ResNet architectures to enhance the detection of foreground galaxy-obscured lenses. Our approach consists of two main stages: first, the U-Net model separates the foreground galaxy light from potential lensing signals, creating residual images that highlight the lensing features. Next, the ResNet module performs binary classification on these residual images to detect lensing signals. *Results.* We evaluated the hybrid search method with real observational data to demonstrate its effectiveness, achieving a recall of 71.5% and a 4.5% false positive rate at a confidence threshold of 0.6. Applying this method to over 638,398 galaxy samples from the Kilo-Degree Survey Data Release 4 and conducting thorough inspections, we identify 88 Class A, 322 Class B, and 1,758 Class C candidates. *Conclusions.* This hybrid approach significantly enhances the completeness of existing strong gravitational lensing searches and shows great potential for improving future astronomical surveys.

Vision-language-action (VLA) policies solve the same manipulation task through different action interfaces, but task success alone does not establish whether their physical executions agree. We study cross-policy end-effector geometry in 15,000 closed-loop LIBERO rollouts from four policies. The primary clean-condition analysis forms 3,600 configuration-matched, and therefore dependent, policy pairs. Both-success pairs have a median normalized dynamic time warping distance of 0.0120 m versus 0.0380 m when exactly one policy succeeds. This ordering holds in every task, every policy pair, and nine sampling and band-limited representations; however, the ratio varies severalfold across representations, so we report the direction rather than a fixed multiple. Both-failure pairs are more separated again but rest on thin, uneven support, so we report them as exploratory. Within successful executions, partner replacements separate more across tasks than across initial states. A matched baseline still reveals measurable, heterogeneous residual policy differences, so a low cross-policy distance does not imply interchangeability. Successful executions sit about as far from same-task demonstrations as those demonstrations sit from each other, compatible with task-associated geometry without separating training-data overlap from task constraints. A common 72-action window preserves the ordering but reduces its magnitude; endpoint and duration adjustment likewise leaves a positive mixed-outcome coefficient relative to both-success pairs, though its magnitude is specification-dependent. Under composite visual stress, policy rankings and pair composition change together.

Relic galaxies are the descendants of high-redshift compact quiescent systems. We present the first spatially resolved spectroscopic study of J1447-0149, a massive relic at $z=0.21$, observed with MUSE+AO. We characterize its kinematics and stellar population properties to probe its spatially resolved mass assembly history. We measured stellar kinematics with sub-kpc bin sizes, covering $\sim 1.4$ effective radii. We then used a coarser three-bin configuration informed by the kinematics to recover the higher-order velocity moments, $[\alpha/{\rm Fe}]$, stellar age and metallicity. We reconstructed the star formation history and computed the degree of relicness (DoR). MUSE data reveal a velocity gradient, showing that J1447-0149 is not purely pressure supported. The velocity-dispersion field displays a central peak, reaching $\sigma_\star=233\pm13\,{\rm km\,s^{-1}}$, substantially larger than previous seeing-limited measurements ($\sigma_{\star} =187 \pm 9\,{\rm km\,s^{-1}}$). The $h_3$–$V_\star$ anti-correlation and mildly positive $h_4$ values support a composite structure, with a rotating stellar component surrounding a compact dynamically hot core. This central, dispersion-dominated region is also the oldest and most metal-rich component. Its SFH rises rapidly, with the stellar mass assembled within $\sim2\,{\rm Gyr}$ after the Big Bang, and reaches ${\rm DoR}=0.9^{+0.1}_{-0.2}$. The two outer bins have a DoR value of ${\rm DoR}=0.8\pm0.2$, consistent with the central bin, but possibly indicating slightly longer formation times. Spatially resolved spectroscopy has been crucial to confirm the relic nature of J1447-0149, linking resolved morphology, kinematics, and stellar populations to constrain the early assembly of its central spheroid and surrounding disk.

Let $\mu$ be a positive Borel measure on $[0,1)$ and $\omega$ a radial weight. In this paper we consider the Cesàro-type operator $C_{\mu,\omega}$ induced by the reproducing kernel $B^{\omega}$ of the weighted Bergman space $A^2_{\omega}$, given by $$ C_{\mu,\omega}(f)(z)=\int_{0}^{1}f(tz)B^{\omega}_t(z)\,d\mu(t), \quad z \in \mathbb{D}, $$ for functions $f$ analytic in $\mathbb{D}$. Under the assumption that $\omega$ satisfies a natural doubling property, we study the boundedness of $C_{\mu,\omega}$ acting on several spaces of analytic functions, including Hardy spaces $H^p$ and weighted Bergman spaces $A^p_{\nu}$. For $0<p,q<\infty$ and a two-sided doubling weight $\nu$, we completely characterize when $C_{\mu,\omega}: H^p \to H^q$ and $C_{\mu,\omega}: A^p_{\nu} \to A^q_{\nu}$ are bounded in terms of the interplay of tail integrals or moments of the inducing weights and the measure $\mu$. Many of the results obtained are new even in the setting of standard weights or when the Bergman reproducing kernel is replaced by the Cauchy kernel. In addition, we consider $C_{\mu,\omega}$ acting on $H^{\infty}$, Korenblum spaces and weighted Hardy spaces.

Recent Joint-Embedding Predictive Architectures (JEPAs) prevent representation collapse by constraining learned representations to follow a prescribed target distribution, such as an isotropic Gaussian or the uniform distribution on a hypersphere. Klindt et al. (2026) showed that, under their Euclidean assumptions, matching a Gaussian target can recover Gaussian latent variables up to a linear transformation, and that the Gaussian is the unique distribution with this guarantee. We extend their analysis to latent variables supported on embedded Riemannian manifolds and derive conditions on the latent geometry and positive-pair dynamics under which alignment and exact distribution matching guarantee linear recovery. In particular, when the latent variables are uniformly distributed on a sphere and the representations are matched to the same spherical distribution, every optimal representation recovers the latent state up to an orthogonal transformation. This shows that Gaussian uniqueness is not a universal property of distribution-matched JEPAs: non-Euclidean latent geometries can admit other linearly recoverable distributions. We further derive an approximate-recovery bound that is strictly tighter for the spherical world than for the Gaussian world. Experiments on Gaussian, spherical, and toroidal latent spaces show that geometrically compatible targets yield better linear recovery when optimization succeeds, whereas mismatched targets distort the latent structure. This advantage persists in high-dimensional Clifford-torus worlds.

We propose a framework to analyse how strongly different linguistic relations are linearly encoded in language model embedding spaces. We formalise linear encoding via a constrained linear approximation over related and unrelated word pairs and apply this to an extended BATS dataset covering inflectional, derivational, lexicographic, and encyclopedic relations in GloVe, RoBERTa, and ModernBERT. Our experiments show near-perfect linear encodings for inflectional and derivational relations, but substantially higher errors for lexicographic and encyclopedic relations, especially for one-to-many and many-to-many associations. We also find that RoBERTa and ModernBERT generally encode relations more linearly than GloVe. These results indicate that our framework can reveal which relational structures are most linearly accessible in embeddings, offering a compact tool for probing and comparing relational geometry across models.

While hybrid organic-inorganic halide perovskite solar cells have achieved remarkable certified efficiencies, their widespread industrial and societal adoption is hindered by instabilities against light, heat, and moisture. A strategy to mitigate issues, such as moisture sensitivity, involves depositing 2D perovskites on 3D thin films for passivation, but their precise impact on cell performance requires detailed understanding. This work employs atomistic first-principles simulation, based on hybrid functionals, to investigate the structural and electronic properties of 2D/3D interfaces. Specifically, it focuses on interfaces formed by (PEA)2PbI4 (PEA = C6H5CH2CH2NH3, as 2D perovskite) and complex 3D perovskites (Cs0.125MA0.14FA0.735Pb(I0.87Br0.13)3, with MA = CH3NH3 and FA = CH(NH2)2) which are ones of the most used perovskites. The approach is based on optimized hybrid functional methods to consistently determine work function (WF), electron affinity, and band offset (EBO) across different layers. Preliminary results demonstrate that WF are strongly dependent on the cleavage and chemical nature of the surfaces. Furthermore, the creation of interfaces significantly impacts macroscopic potential, with a noticeable slope linked to the polarization of the 3D materials due to ionic substitutions. The band alignment is also highly sensitive to the termination and chemical nature of the perovskites, with valence and conduction EBOs varying from 0.2 to 0.7 eV and of approximately 0.25 eV, respectively. This ongoing work aims to provide a systematic description of these effects, with further investigation into the impact of dimensionality loss on perovskite stability.

Symmetry in the context of equivalence or isomorphism is a fundamental and natural concept in any study of discrete structures. Symmetries are also important for non-discrete structures, but their treatment can be more challenging and is perhaps therefore often overlooked. This holds for many studies of complex Hadamard matrices, that is, matrices with unimodular complex entries satisfying the equation $HH^{\dagger} = nI$, where $H^{\dagger}$ is the conjugate transpose of $H$. In the current work, equivalence of complex Hadamard matrices is considered, and algorithms for determining equivalence of matrices and the automorphism group of a matrix are presented. The algorithms are used to establish the automorphism group of a large number of complex Hadamard matrices from the literature.

We investigate particle acceleration during the early stages of a supernova explosion via a resonant interaction between electromagnetic waves and quantum waves associated with particles. For typical progenitor masses of $(8; 12; 20)\times M_s$, we find that this mechanism can accelerate protons to energies of up to $3\times 10^{14}$ eV. Interestingly, despite the continuously declining luminosity, the particle energy initially increases, reaches a maximum, and subsequently decreases, reflecting the characteristic behavior of the resonant acceleration mechanism.

FarmerChat is Digital Green's farm advisory service for smallholder farmers. When something looks wrong with a crop, the farmer takes a photograph and sends it, and that photograph is the whole question: no symptom described, no crop named, often no text at all. The service has to determine whether the picture can be used, what crop it shows, and what is wrong with it, from images taken on cheap phones in a field, in poor light and with a moving camera. The system doing this today cannot be adjusted. It has no adjustable thresholds for photograph rejection, crops and problems cannot be added, and there is no confidence cut-off to set. We study about 1.16 million photographs sent to FarmerChat from Ethiopia, India, Kenya and Nigeria. The production quality gate rejected 46.8% of the images it judged, over a quarter of those reaching diagnosis returned no crop name, and 35.8% of the labelled problems filed under "disease" are pests, identifiable without the crop. We therefore split the work into three stages: a quality gate (M0), a crop detector (M1), and a disease or pest detector (M2). Route A fills all three with one fine-tuned vision-language model (Qwen3-VL-4B) answering in a single call. Route B fills each with a small specialist model (DaViT, YOLO26). We replace our production GPT-4o quality gate with a small MobileNetV3 gate at 86.9% F1 in 12 ms. On one test set scored the same way for every system, a hierarchical DaViT-Base achieves 95.41% crop accuracy against 91.46% for the production baseline. It also leads on diagnosis and never declines to answer, while every language model in the comparison leaves a large share of rows with no diagnosis. The fine-tuned model retains two capabilities the specialists do not have: one call for all three stages, and a request for a better photograph when the image cannot support an answer.

Fine-tuning Vision-Language-Action (VLA) models commonly relies on human teleoperation demonstrations, while reinforcement learning (RL) with sparse binary rewards faces an exploration challenge when successful trajectories are rarely sampled. We propose SynthDemo-RL, a teacher-student framework in which an automated teacher converts simulator-privileged state into successful manipulation trajectories, a VLA student is distilled from them by supervised fine-tuning (SFT), and PPO with binary task-success rewards refines the student. We study reward coverage, the fraction of tasks for which at least one success is observed under the fixed evaluation protocol, as a complement to the average success rate. On LIBERO-PRO, a public benchmark of perturbed LIBERO tasks for which no demonstrations exist, 27 of 57 scored tasks are at exactly 0% success for a pi_0.5 policy fine-tuned on the original LIBERO tasks. Direct PPO from this policy, under the same PPO recipe and the same RL compute as SynthDemo-RL's refinement stage, rescues 10 of these 27 tasks and leaves 17 at 0%. SynthDemo-RL, with 50 synthesized trajectories per task and no new human demonstrations, rescues all 27 and reaches average success rates of 97.8% and 97.1% on the Position and Task axes of LIBERO-PRO, respectively. On standard LIBERO, the same pipeline reaches 96.0% with no human demonstrations, within 1.7 points of pi_0.5 trained on 50 human demonstrations per task. We further validate the pipeline on RoboTwin 2.0 and verify that trajectories from a policy trained in a MuJoCo twin execute open-loop on a physical robot.

Let $\sigma\mathrm{Mex}(n)$ and $\sigma_e\mathrm{Mex}(n)$ denote the sum of minimal excludants and sum of even minimal excludants over all overpartitions, respectively. In this work, we study these two combinatorial objects from an arithmetic perspective. We prove that, for $n\geq 0$, $\sigma_e\mathrm{Mex}(n)\equiv\sigma\mathrm{Mex}(n)-\bar{p}_{\geq 2}(n)\pmod{2^2}$, where $\bar{p}_{\geq 2}(n)$ denotes the number of overpartitions of $n$ with all parts at least $2$, and obtain relation with basic hypergeometric series. Furthermore, we prove the asymptotic behavior of $\sigma\mathrm{Mex}(n)$, $\sigma_e\mathrm{Mex}(n)$, and $\bar{p}_{\geq 2}(n)$ as $n\to\infty$. In particular, we prove that $\sigma\mathrm{Mex}(n)\sim 2\,\sigma_e\mathrm{Mex}(n).$

A prospective search for dark photons decaying into collimated, displaced muon pairs is presented for the electron-positron stage of the Future Circular Collider, FCC-ee. Assuming the full luminosity of the Higgs run at 240 GeV, the study probes a broad range of dark photon masses and couplings. The signature comprises two jets from a Z boson decay and two muon pairs from dark photons produced in Higgs decays. A kinematics-based selection achieves zero background while retaining high signal efficiency. Expected limits are set on the Higgs boson branching ratio to dark photons as a function of the dark photon mass and coupling.

Hamiltonian normalizing flows are attractive generative models because their phase-space maps are invertible and volume preserving, but most neural constructions are formulated in Euclidean space. We introduce Riemannian Neural Hamiltonian Flows, which combine the fixed kinetic energy of a Riemannian manifold, a learned scalar potential, and an explicit geodesic integrator. We then study the interpretability of the learned potential through a thermodynamic reading in which the momentum variance plays the role of a temperature. The matched potential, whose Boltzmann distribution is the data, is the potential whose force balances the pressure of the data. The output of one pass of the flow is the Boltzmann distribution of the learned potential multiplied by a memory factor, so that the learned potential is the matched potential whenever the pass forgets its starting point. Numerical experiments on Euclidean, hyperbolic, and spherical spaces show competitive sample quality and numerical cost against a Riemannian continuous normalizing flow, and confirm the interpretability of the learned potential. We then show that this reading has a computational use. When the energy of the data is known but expensive, the landscape learned from existing samples is a surrogate energy for Hamiltonian Monte Carlo, allowing exact sampling with significant acceleration. We test this approach on the localization of a neutrino source from public IceCube data.

A hybrid framework combining the deformed Gamow-like model ($\mathrm{DGLM}$) with the Tabular Prior-data Fitted Network ($\mathrm{TabPFN}$) is developed to improve half-life predictions for two-proton emission, proton emission, $\alpha$ decay, and cluster radioactivity. A total of 583 radioactive nuclei are investigated, including 17 two-proton emitters, 42 proton emitters, 498 $\alpha$ emitters, and 26 cluster emitters. Among the four considered models, $\mathrm{DGLM}^{b}+\mathrm{TabPFN}$ achieves the best overall performance, with $\sigma_{\mathrm{RMS}}=0.423$, corresponding to an improvement of approximately $82.2\%$ over $\mathrm{DGLM}^{b}$. The model parameters are optimized for each decay mode using the least-squares method. After introducing $\mathrm{TabPFN}$, the prediction errors for proton emission and $\alpha$ decay are reduced by approximately $80.6\%$ and $87.6\%$, respectively. For $\alpha$ decay, the training, test, and overall RMSEs are 0.208, 0.305, and 0.240, indicating good generalization capability without evident overfitting. The model also reproduces the systematic evolution of $\alpha$-decay half-lives and the shell-closure effect around $N=126$. These results demonstrate that combining $\mathrm{DGLM}$ with $\mathrm{TabPFN}$ significantly improves the accuracy and robustness of radioactive-decay half-life predictions while retaining the physical interpretability of the original model.

A family of permutations in $S_n$ is called even-intersecting if every two distinct members agree in an even number of positions. Let $M(n)$ denote the maximum size of such a family. For even $n$, we prove that $$n!!\leq M(n)\leq e^{\frac{n}{2}+o(n)}n!!,$$ improving the bound obtained from a theorem of Cameron, Deza and Frankl (1987) by an exponential factor. This problem may be viewed as a permutation analogue of the classical Eventown problem for set systems. For odd $n$, we give a construction yielding $M(n)\geq n^2/4$. We further extend this construction to obtain $$ M(n)\geq\bigl(n-\sqrt{n-1}\bigr)^2 ,$$ whenever $n=(q+1)^2+1$ and $q$ is an odd prime power. The latter bound asymptotically matches the upper bound $M(n)\leq(n-1)^2+1$ obtained by Cameron, Deza and Frankl.

We develop a categorical framework for Lie-Rinehart monoids and their weak modules in a symmetric monoidal category. Using crossed homomorphisms, we construct a natural action of the monoidal category of modules over a Lie monoid on the category of weak Lie-Rinehart modules, thereby obtaining categorical versions of the Shen-Larsson functors. We further characterize the conditions under which the category of weak modules admits a monoidal structure and identify the corresponding condition for the associated functors to be strict monoidal. A dual theory for Lie- Rinehart comonoids and weak comodules is developed using cocrossed homomorphisms. Combining the module and comodule constructions, we obtain a bimodule category structure on the category of weak modules. Finally, we specialize the general framework to the symmetric monoidal category of super vector spaces, recovering Lie-Rinehart superalgebras and their associated Shen-Larsson-type constructions.