Papers

Objective. This work aims to accelerate our four-dimensional (4D) proton pencil beam delivery strategy, which incorporates respiratory motion into a dynamic treatment plan, to improve dose conformity and treatment efficiency for gantry-less and magnet-free scanner designs. Approach. To accelerate the generation and adaptation of 4D treatment plans, we propose a conditional hybrid ResNet18-Transformer model for predicting pencil beam weights. The model predicts either the full set of pencil beam weights or a subset thereof. Main Results. The conditional model can successfully predict the remaining beam weights of a treatment, and the results suggest that extending this approach to full treatment prediction is feasible but requires further investigation. Significance. The acceleration of 4D treatment generation via pencil beam weight prediction takes us one step closer to the feasibility of treating mobile targets with simplified, gantry-less, and magnet-free scanner designs. Reducing system complexity while preserving dosimetric conformity may offer a pathway toward more accessible and cost-effective proton beam therapy for motion-affected tumours. Our code is available here: https://github.com/NairVonMuehlenen/Pencil-Beam-Weight-Prediction

Learned world models are becoming essential to general-purpose agents: by predicting action consequences, they support planning and decision-making while reducing reliance on costly trial and error. This reliance creates a fundamental ambiguity: when a world-model-guided decision fails, the trajectory alone may not reveal whether the agent's decision rule or the world model caused the loss. We formalize this failure-attribution problem as a counterfactual decomposition of return loss and prove that its components are not identifiable from passive interaction, even for finite-horizon planners. This obstruction motivates Dual-Frontier, a learning principle that admits a world-model-guided decision only when its predicted advantage exceeds a certified bound on decision-relevant world-model error; otherwise, evidence is allocated to world-model verification. Action-conditioned value bounds and a closed-loop extension guarantee non-decreasing return for admitted decisions. Calibrated gates and simultaneous confidence sequences support adaptive evidence reuse, with sufficient and necessary verification bounds. Controlled learned-model experiments validate the predicted failure modes and certification behavior, while cross-backbone tool-use benchmarks instantiate the same verify-then-promote rule in realistic agent world-model pipelines, consistently improving decision quality and reliability.

Physical-condition diversity is largely missing from current benchmarks for robot manipulation. While large-scale simulation benchmarks increasingly incorporate variations in object appearance, scene layout, and visual observations, they typically keep the underlying physical parameters fixed. As a result, important sources of real-world variability, such as changes in mass, friction, and joint dynamics, remain largely untested. We introduce RoboTwin-Phys, a physics-diverse benchmark that treats physical-condition diversity as an explicit dimension of robot manipulation evaluation. The benchmark continuously varies 13 physical attributes within physically plausible ranges, providing a unified setting for evaluating policies across diverse physical operating conditions. We further release more than 5,000 expert demonstrations with ground-truth physical parameters, enabling physical-attribute estimation, condition-aware modeling, and physics-conditioned policy training. Evaluations of representative WAMs and VLAs reveal a substantial robustness gap: models that remain effective under existing visual and layout randomization can degrade markedly under changes in physical conditions. RoboTwin-Phys provides the benchmark, data, and evaluation protocol needed to systematically measure and improve robustness to physical-condition diversity in robot manipulation.

Single-beam ptychography (SBP) requires overlapping scan positions for reliable reconstruction, and imaging larger areas demands more measurements. Multi-beam ptychography (MBP) illuminates several regions simultaneously, but its measurement gain at a fixed resolution remains unclear when diffraction intensities from different beams overlap on the detector. Using numerical simulations, we determined the minimum number of patterns needed to reach a target resolution by varying the scan step size for SBP and fully overlapped MBP with up to 15 beams. We define gain as the pattern count for repeated SBP scans divided by that for MBP at the same total imaged area and achieved resolution. Although the required MBP pattern count increased approximately linearly with beam number, it remained below that of repeated SBP scans. At 67% of the spatial Nyquist frequency using a one-bit threshold, fully overlapped MBP achieved a gain of approximately two. Detector cropping and lower-resolution targets reduced this gain, showing its dependence on usable diffraction information and the reconstruction criterion. Because overlapping intensities provide no spatial identification of individual beam contributions, this gain is a conservative benchmark; separation on the detector offers a route to larger gains.

Causal tabular foundation models amortize effect estimation across synthetic mechanisms, but latent-effect supervision rewards posterior shrinkage rather than encoding the repeated-sample response needed in a fixed deployment population. We introduce fluctuation-supervised pretraining (FSP): each synthetic table is labeled by its average treatment effect plus its efficient influence-function fluctuation; deployment remains a frozen forward pass. Along the path $T_{\lambda,P}=\theta(P)+\lambda P_n\psi_P$, we prove an endpoint transition: every fixed $\lambda<1$ retains label ambiguity of order $(1-\lambda)^2/n$, whereas full fluctuation makes the Gaussian label observable and reduces optimal finite-stratum causal label-prediction risk to order $n^{-2}$. A finite-pretraining bound combines label, network, episode-sampling, and optimization errors; its sampling defect controls fixed-mechanism bias, mean squared error, variance, Gaussian approximation, and, with variance-head accuracy, studentized coverage. Complementary lower bounds separate local $n^{-1}$ ATE risk from the $\log N/M$ excess risk of generic finite-dictionary episode learning. Experiments trace the learned sampling response. Across 24 nonlinear continuous-covariate cells at trained context lengths, continuous-row FSP lowers checkpoint-mean macro RMSE by 7.0% versus S-learner and wins all 12 weak-overlap cells; validation-selected Summary FSP deploys $11.6\times$ faster per table in our warm one-thread benchmark. Under effect shift, matched Raw FSP lowers mean-checkpoint RMSE by 54.2% and teacher defect by 99.0% versus latent-effect supervision, and RMSE by 10.2% versus the released CausalPFN-S checkpoint. Known-effect semisynthesis tests coverage; two randomized-study evaluations show that lower RMSE can coexist with residual attenuation.

The manipulation of Deformable Linear Objects (DLOs) such as cables poses a significant challenge for automation due to their infinite degrees of freedom and non-linear dynamics. In this paper we present a machine learning based optimal control approach for the manipulation of DLOs. This approach is divided into two main components: modeling and control. For modeling the dynamics of the DLO, we propose a learning based approach using a bidirectional Long Short-Term Memory (biLSTM) network. The biLSTM network is trained on synthetic data generated by the MuJoCo physics engine. For manipulating the DLO, a model predictive control strategy that employs Model Predictive Path Integral (MPPI) control is selected. The proposed approach is evaluated through simulation and experiments. The results demonstrate the effectiveness of the proposed method in achieving accurate and efficient manipulation of DLOs.

Large Language Models (LLMs) have been used in various industries. However, ensuring their compliance with complex laws and regulatory frameworks remains a great challenge. Existing evaluation paradigms mainly rely on static benchmarks that suffer from three severe limitations: First, the compliance rules being used do not comply with the requirements of Artificial Intelligence (AI) laws and regulations; Second, they only handle apparent, explicit compliance risks, leaving implicit and covert compliance risks undetected; Third, they fail to track the systematic propagation of risks along logical dependency chains or evaluate compliance within nuanced, context-based real-world scenarios. To bridge this critical gap, we introduce EADC, a novel advanced evaluation benchmark of LLMs based on an AI compliance knowledge graph and AI compliance legal experts. By mapping abstract legal rules into structured logical multi-relational graphs, our framework enables automated, evolving agents to distill and synthesize highly sophisticated adversarial scenarios. This compliance benchmark is reviewed and corrected by human AI legal experts throughout the whole process. The resulting dataset (4,435+ QA pairs) provides an extensive, multi-dimensional taxonomy covering critical regulatory frontiers, including bias and discrimination, fairness, personal privacy protection, and values. Crucially, our compliance dataset moves beyond shallow string-matching by incorporating contextual long-horizon interactions and logic-driven hazard chains, capturing deeply embedded compliance anomalies that bypass traditional filters. Experiment evaluations demonstrate that our framework exposes critical regulatory blind spots in state-of-the-art LLMs, offering a rigorous, AI laws and regulations-aligned benchmark to safeguard high-level and deep compliance in the application of LLMs.

Distributed state estimation algorithms have been extended to switching networks, which model unreliable communication networks. Yet existing results apply only to specific classes of systems, such as neutrally stable systems. In this paper, we analyze a distributed observer under the assumption that the system matrix commutes with the coupling matrices. This not only enables a refined analysis that leads to a necessary and sufficient condition for stability over switching networks, but also covers a broader class of systems than existing results, including unstable systems such as vehicular platoons.

We investigate the challenges of enabling effective collaboration between human operators and heterogeneous autonomous agents in complex, dynamic environments by developing an interaction platform that allows study of operator behavior and supports intent inference and decision-making using state-of-the-art frameworks. We demonstrate the extent to which the operator's perception, decisions, and actions could be supported by autonomous systems during search-and-rescue operations with our platform.

This is an essentially derivative note, whose goal is to interpret the 'whole-cube' bound of OpenAI for binary codes in a possibly somewhat more accessible way. This is attained, in part, by connecting it to some previously known results. All of the heavy technical lifting in the interpretation below is also due to the OpenAI language models ChatGPT 5.6 and ChatGPT 6. With that, we hope that the statements of the main results, the ensuing discussion, and the arguments themselves may be of some interest.

We address three problems on separable quotients of topological groups posed by Leiderman, Morris, and Tkachenko in \cite{LMT} published on Israel Journal of Mathematics. First, we construct in ZFC a connected Baire Pontryagin-reflexive dense subgroup of $\T^{\cc}$ whose countable subgroups are $h$-embedded and whose uncountable subgroups are dense. Its underlying abstract group is the circle group, and all its compact subsets are finite. Second, we construct a zero-dimensional Baire Pontryagin-reflexive example with the same subgroup properties whose underlying group is free abelian of rank $\cc$. Both examples have no nontrivial separable Hausdorff quotient. Third, for the group constructed in their Theorem~3.5, we determine every closed subgroup of every finite power up to an integral change of coordinates and prove that every countable subgroup of every Hausdorff quotient of a finite power is $h$-embedded and closed. The same conclusions hold for our free Baire reflexive example. These results answer Problem~1.25 negatively, Problem~3.12 affirmatively and realize all three regularity properties in Problem~3.14 simultaneously in \cite{LMT}.

Language-model agents often reach a working solution and then fail to consistently deliver it. We study runtime policies: targeted natural-language instructions and action denials applied by the agent harness at states that preceded observed failures, without changing model weights or the user prompt. With this, keeping capability constant, we observe a meaningful unlock in delivered reliability. Across the complete 87-task Terminal-Bench 2.1 suite, with two attempts per task, policies increase repeated success (pass^2) in all three GPT-5.6 tiers: 50.6% to 54.0% for Luna, 55.2% to 60.9% for Terra, and 64.4% to 73.6% for Sol. Sol's best-of-two success changes by 1.2 points while repeated success rises by 9.2, showing that policies chiefly convert reachable solutions into dependable delivery. We further cover 14 tasks under Terra's frozen portfolio. Policy-guided Terra reaches 71.4%, compared with 64.3% for unassisted Sol, at about half the cost, demonstrating how engineering around models could unlock dependability for a use case. To isolate the mechanism we run a randomized five-arm experiment: real policies reach 61% on eligible tasks, versus 39% without a policy, 36% with a timing-matched sham, and 39 to 43% with generic verification or reconsideration. The intended corrective behavior appears in 22 of 24 coded policy attempts, against at most 14 in any other arm. Runtime policies are therefore a practical reliability layer: they make capabilities an agent already possesses substantially more repeatable.

We introduce communication-complexity lifting techniques into the study of recognizable picture languages. As an application, we resolve a long-standing open problem of Anselmo et al. (2006) by constructing a language in UREC whose complement does not belong to REC. Our lower-bound argument is inspired by the communication-complexity approach to unambiguous automata of Göös et al. (2022), although its implementation in the setting of picture languages requires substantially different technical ingredients.

One of the challenges in representational learning is how to encode part-whole hierarchies in a neural net. Prior works rely on flattening tree-like structures into string-like sequences and training a sequence-to-sequence model via autoregression. While such a representation works for parse-trees in NLP, it is not entirely clear how to make it work for images. Thus, we propose a geometric primitive called canonical locks. The key idea is that parts/wholes can be modelled as higher-dimensional vectors ($d \geq 4$), and information can be encoded in their relative phase differences. Inductively, the net consists of positionally-bound bottom-up and top-down neural fields, which drive each other to achieve a state of thermal equilibrium. Additionally, we show the existence of a few symmetrical configurations in the net. The computational iterations taken to break these symmetries depend on the angle between parts/wholes arranged on a disk (or more precisely a ring) in higher dimensions. It also appears to have connections to the psychological phenomenon of mental rotation.

Improper edges were introduced by Shor to refine Cayley's formula for rooted labeled trees. Zeng established a connection between Shor's refinement and the Ramanujan polynomials. Let $\mathscr{T}_n$ denote the set of rooted labeled trees on $[n]=\{1,\ldots,n\}$. We prove that the number of improper edges in a uniformly random tree in $\mathscr{T}_n$ is asymptotically normal as $n\to\infty$, with mean and variance asymptotic to $\mu n$ and $\sigma^2 n$, respectively, where $\mu=e-2$ and $\sigma^2=e^2-3e+1$. This phenomenon was observed by Chen, and the proof presented here was developed through human–AI collaboration.

For integers $n\ge3$ and $2\le\Delta\le n-1$, let $\lambda_1(n,\Delta)$ be the maximum adjacency spectral radius among all connected nonregular graphs of order $n$ and maximum degree $\Delta$. Liu conjectured that for each fixed integer $\Delta\ge3$, \[ \lim_{n\to\infty}n^2\bigl(\Delta-\lambda_1(n,\Delta)\bigr)= \begin{cases} (\Delta-1)\pi^2/4,&\text{if $\Delta$ is odd};\\ (\Delta-2)\pi^2/2,&\text{if $\Delta$ is even}. \end{cases} \] He proved the case $\Delta=3$ and $\Delta=4$. We prove the conjecture when $\Delta\ge5$ is odd.

Symmetry breaking at crystalline boundaries can enable electronic responses that are forbidden in the bulk. Here, we investigate the Berry curvature dipole (BCD) at GaAs(110) surfaces using first-principles calculations. While the BCD vanishes in bulk GaAs due to symmetry constraints, the reduced surface symmetry permits a finite dipole. We show that surface relaxation promotes hybridization between bulk and surface states, which strongly influences the surface BCD. Specifically, in unrelaxed slabs, the BCD arises predominantly from interband coupling among exponentially localized surface states lying within the projected bulk band gap. Surface relaxation shifts these states into the energy range of the bulk continuum, transforming them into surface resonances and promoting hybridization with bulk-like states. This hybridization generates pronounced Berry-curvature hot spots, resulting in an overall enhancement of the BCD. Our results highlight the importance of surface relaxation for accurately describing surface–bulk hybridization, which in turn plays a key role in Berry-curvature-driven responses at crystalline boundaries.

When does a collection of autonomous cells become a multicellular individual? We propose that coherence provides a physical description of this transition. Coherence is treated as a global property arising when distinguishable constituents admit a physically meaningful collective state-space description. Using the center of mass and an interaction-based construction, we show that such collective states can be defined for classical bodies before dynamics is introduced, with normal modes emerging as a particular dynamical realization. We apply this framework to multicellular organization, where cells retain their identities while their independent individuality is replaced by participation in the organized whole. In Dictyostelium discoideum, cAMP-mediated coupling produces population-level collective modes, while starvation provides an experimentally controlled energetic constraint on the transition to multicellularity. The framework yields direct tests through interaction-derived collective eigenstates and the energetic cost of maintaining autonomous versus collective organization. Coherence may thus provide a general physical description of multicellular individuality without requiring microscopic quantum coherence or intrinsic wave character.

Let $\Ke$ be obtained from $K_7$ by deleting two independent edges. We prove that every 5-connected graph on $n\ge7$ vertices with at least $4n-9$ edges contains a $\Ke$ minor, settling Conjecture~1.4 of Dvo\v rák, Norin and Rahman (arXiv preprint 2609.17760v1). The bound is sharp. We prove the stronger statement that every $4$-bilight graph on $n\ge4$ vertices with at least $4n-9$ edges contains either a $\Ke$ minor or a $K_6$ subgraph. Within their reduction framework, we strengthen the rooted-minor theorem. We show that every $4$-light 5-rooted graph of rooted $4$-density at least two has a model with two nonroot vertices and at most one missing edge incident with them. At the critical density, reductions preserve density exactly, which prevents them from creating a new $K_6$ subgraph.

We present a systematic study of semileptonic decays of heavy vector mesons within the Hard-Wall AdS/QCD framework. Semileptonic decays provide a clean environment for testing the Standard Model because the leptonic current is well understood, while the hadronic part is encoded in transition form factors that reflect non-perturbative QCD dynamics. The processes under consideration include: \( \psi \to D^{*-} ( D^{-} ) \ell^{+} {\nu}_{\ell} \), \( D^{*0} \to \pi^{-} \ell^{+} {\nu}_{\ell} \), \( D^{*+}_{s} \to K^{0} \ell^{+} {\nu}_{\ell} \), \( D^{*0} \to \rho^{-} \ell^{+} {\nu}_{\ell} \), \( B_c^{*+} \to B^{*0} \ell^{+} {\nu}_{\ell} \), \( B_c^{*+} \to \psi \,\ell^{+} {\nu}_{\ell} \), \( B^{*-} \to D^{*0} \ell^{-} \bar{\nu}_{\ell} \), \( B^{*0} \to D^{*+}(D^{+}) \ell^{-} \bar{\nu}_{\ell} \), \( B^{*0}_{s} \to D^{*+}_{s} (D^{+}_{s}) \ell^{-} \bar{\nu}_{\ell} \), \( \psi \to D^{*-}_{s}(D^{-}_{s}) \ell^{+} {\nu}_{\ell} \), \( D^{*0} \to K^{*-} (K^{-}) \ell^{+} {\nu}_{\ell} \), \( B_c^{*-} \to D^{*0} \ell^{-} \bar{\nu}_{\ell} \), \( \bar{B_{s}}^{*0} \to K^{*+} \ell^{-} \bar{\nu}_{\ell} \), and \( \bar{B}^{*0} \to \rho^{+} \ell^{-} \bar{\nu}_{\ell} \). These decays correspond to four different quark-level transitions: \(c\to d\), \(b\to c\), \(c\to s\), and \(b\to u\), allowing us to explore a broad range of flavor dynamics.\\ Using the Hard-Wall AdS/QCD model, we compute the relevant transition form factors as functions of the momentum transfer \(q^{2}\). The framework provides analytic expressions for meson wave functions and decay constants, which serve as inputs for the form-factor calculations. From these form factors, we evaluate the differential and integrated branching ratios for each decay mode. Where possible, we compare our predictions with results obtained from other non-perturbative approaches.

Point cloud generation has emerged as a crucial task for accurately capturing and reproducing the complexity of the physical world. However, existing generative approaches, predominantly relying on Transformers and Variational Autoencoders (VAEs), frequently ignore the continuous, non-grid topologies inherent to 3D spaces. Although the integration of graph-based structures has yielded significant benefits in related discriminative vision tasks, such geometric architectures remain noticeably absent from 3D generative modeling. To address this gap, we introduce EMERGE (Equivariant Multi-scale GNN for Resolution-agnostic point cloud GEneration), the first fully $SE(3)$-equivariant graph-based diffusion backbone explicitly designed to generate point clouds while preserving continuous spatial symmetries. Our framework bypasses the rigid resolution dependencies of standard generative pipelines, enabling zero-shot inference at multiple, arbitrary spatial resolutions. Extensive empirical evaluations demonstrate that EMERGE achieves State-of-the-Art generation quality across standard metrics, while the strong inherent geometric inductive biases enable significantly faster training convergence compared to existing baseline methods.

Compliant arterial wall mechanics, contributing to the Windkessel effect in the carotid artery (CA), have significant impact on hemodynamic patterns and surface shear indicators for cardiovascular diseases, e.g. atherosclerosis. In this study, we extend the linear elastic Fluid-Structure Interaction (FSI) framework to account for nonlinear strain-dependent wall behavior. The model incorporates a Young's modulus generalized from tensile tests on silicone phantoms to capture the nonlinear stress-strain relation of arterial tissue. The final computational model, using a resistance-type boundary condition and in vitro measured stress-strain relation is validated against both, in vitro assessed silicon CA phantom as well as published clinical data on the flow splitting to the daughter branches in CA bifurcations. To better reflect physiological conditions, our model is subsequently extended to incorporate prestress of patient-specific geometries, and clinically measured stress-strain relations, followed by validation against clinical CA data. The present study demonstrates the feasibility of strain-dependent Young's (elastic) modulus as a means to enhance the capacity of the linear elastic framework to accurately represent the physiologically nonlinear mechanics of arterial walls, striking a balance between implementation effort and physiological fidelity. This approach yields realistic strains, volumetric inflation behavior and nonlinear pressure-volume relationships. Furthermore, the study reveals the importance of proper outlet boundary conditions and the shortcomings of resistance-type boundary condition in patient-specific modeling, leading to non-physiological pressure profiles and non-physiological temporal flow splitting.

Explanations are central to causal reasoning, and cognitive science has long established that the human drive to explain is itself a mechanism for learning about causality. Despite this, learning from those abductive signals is largely ignored in artificial intelligence. While explainable AI (XAI) increasingly draws on causal models to generate explanations, the converse direction about what explanations can do for causality remains largely unexplored. To fill this gap, we propose xWhyL, a formal framework connecting causality and XAI by learning causal models from explanations. We develop a mathematical theory that translates explanations into a learning signal complementary to observational data, and demonstrate how it enables overcoming the limits of observational causal discovery. As explanations can be derived from incorrect beliefs and clash with data, a tension we call the Causal Tug-of-War, we prove conditions under which our framework rejects misspecified explanations rather than absorbing them. Our practical instantiation, Causal Interactive Learning (CIL), shows how expert explanations can efficiently support causal discovery and distinguish correct from incorrect explanations.

The stellar binary systems are classical tools for studying dynamics, and tidal circularization is one of the processes taking place in these. During the last few years, several dozen systems have been published supposedly having orbital periods shorter than 1 d, and have also been published as having eccentric orbits. Such a configuration is due to their spatial closeness, and the tides very improbable. Therefore, we performed a thorough analysis of all these eclipsing binaries (>140), showing that the vast majority of the published systems (> 98%) are in fact circular. Especially, the eclipsing binaries identified and published from the Gaia DR3 catalogue suffer from a lack of data, and about 50 per cent had incorrectly derived periods. This mostly incorrect identification of the eccentric orbits is due to automatic pipelines and routines running without human checking/validating, and also due to the large number of systems with (evolving) spots on the surfaces of either of the stars. Only two eccentric orbits were found below the 1-d period limit, while the star TIC 1190662 with an orbital period of about 0.888 d has a surprisingly large value of eccentricity about 0.21.

Conversational agents often express answers in a uniformly confident register. We test whether expressed uncertainty, provenance-aware assertion, and explicit belief revision can be implemented as a behavior layer over a fixed language model; we do not test believability or trust. The layer combines three epistemic states, per-claim confidence and typed provenance, a provenance-gated expression rule, and a persistent revision store with auditable acknowledgments and partial resistance to false corrections. We evaluate it on a constructed, mechanically scored multi-session benchmark using a synthetic model and Qwen2.5-0.5B-Instruct. The synthetic instrument passes all five checks. On the real model, acknowledgment soundness, a by-construction guarantee, holds in 100% of cases, and true corrections are accepted more often than false ones (0.44 vs. 0.15 on held beliefs; 0.875 vs. 0.420 including rule-accepted corrections of unheld facts), but the pre-specified expression-fidelity, contradiction-separation, and provenance margins fail. A disclosed post hoc analysis shows that expression gated on mean answer-token probability ranks correctness below chance end to end (AUC 0.41, conversation-clustered), whereas gating on sampling consistency discriminates (AUC 0.66). A consistency-gated configuration selected from this finding and evaluated under a separately committed protocol meets the conversation-level manipulation and capability-equivalence criteria and replicates on a redrawn conversation set. The manipulation result is selection-dependent, and both criteria remain unresolved when uncertainty is clustered over the 60 facts. The supported conclusions are limited to the by-construction audit guarantee, store-dependent partial correction discrimination, and a benchmark- and model-specific failure of token-probability gating; scaling the fact base is required before human evaluation.

Water treatment research is expanding rapidly, but much of the knowledge acquired from this research remains scattered across unstructured literature. The field still lacks a dedicated language model that can efficiently capture water treatment-specific domain semantics for large-scale literature mining. Here, we address this by developing WaterBERT, a domain-adapted encoder model designed for semantic representation and structured information extraction from water treatment texts. WaterBERT was developed by continual pretraining on a large-scale water treatment corpus comprising about 2.97 billion tokens. Three fine-tuned models based on WaterBERT were systematically evaluated on downstream tasks, achieving the best overall performance among general-purpose and domain-specific BERT models, with F1 scores of 90.12% for multiclass treatment process classification, 79.50% for named entity recognition, and 74.04% for relation extraction. Beyond these benchmark tasks, we further demonstrated WaterBERT's advantages for large-scale literature processing. Applied to 5,144 Environmental Science & Technology articles, WaterBERT-BERTopic identified coherent, diverse, and domain-specific research topics without predefined categories. Building on WaterBERT, we processed 693,211 abstracts at substantially lower cost than commercial LLMs while retaining competitive extraction performance to construct a structured water treatment knowledge graph. The knowledge graph was then integrated with lexical and dense retrieval to develop a Water Knowledge-Enhanced Retrieval System (WaterKERS), which achieved a relevance score of 77.7, substantially outperforming text-based retrieval baselines (54.7-64.5). Through WaterBERT, this study provides a compact and scalable semantic foundation for large-scale information processing and evidence mapping in water treatment research.

We consider the problem of determining if a given two-dimensional nonnegative integer matrix $M$ is the product of two such matrices, excluding trivial units. A matrix $M$ with no such factorisation is called prime and therefore belongs to the minimal (infinite rank) generator of $2 \times 2$ matrices over the natural numbers, otherwise it is called composite. We also consider the problem of finding a (non-unique) factorisation of a composite matrix. Our results have applications in computational group theory and the theory of codes, where such matrices are called incidence matrices. We analyse the complexity of primality and finding a factorisation for a composite matrix, providing a first efficient algorithm.

We construct the first type of non-Euclidean non-autoregressive neural quantum state (NQS) in the form of the hyperbolic Restricted Boltzmann Machine (HRBM), which is studied in the variational Monte-Carlo (VMC) setting of the Quantum Sherrington-Kirkpatrick (QSK) model whose ground state exhibits volume-law entanglement. Across a 512-fold increase in the Hilbert space dimension corresponding to a system size increase from $N=14$ to $N=24$, HRBM NQS robustly outperforms its Euclidean version, the RBM NQS, in terms of better ground state energy optimization as well as lower Renyi-2 $S_2$ and von Neumann $S_{vN}$ absolute entanglement entropy reconstruction errors. More importantly, for all tested QSK system sizes, HRBM NQS demonstrates a superior expressivity in faithfully reproducing the entire entanglement spectrum of the QSK model from the top eigenvalues down to the tail end across 15 orders of magnitude, while RBM NQS consistently overestimates the sub-dominant modes. This work furnishes a proof-of-concept demonstrating that hyperbolic non-autoregressive NQS ansatze, thanks to the exponential volume of the hyperbolic geometry underlying their constructions, might be more natural at representing volume-law quantum systems than conventional Euclidean NQS. Furthermore, an interesting byproduct of this work is the polynomial scaling result of RBM-type NQS ansatze in the QSK volume-law system as the Hilbert space dimension increases exponentially.

The debate over pairwise and higher-order models is often framed as a contest of expressive power. This framing is misleading. A graph with arbitrary multivariate node functions can reproduce the node-level dynamics of many hypergraph models, but the hypergraph's grouping information does not thereby disappear: it may simply move from the structure to the rule. We separate four notions frequently conflated here: structural representation, functional representability, statistical identifiability, and mechanistic adequacy. We then prove that interaction order, the number of variables that must act jointly in some term of any additive decomposition of a node's update, is the same in every exact representation: no change of structural language can lower it. As a description-length problem, at the unrestricted algorithmic level a fixed compiler redistributes information between structure and rule at constant overhead, so expressiveness alone cannot privilege either language. Preferences arise only relative to explicit model classes, code families, and data. This yields an operational minimum-description-length criterion combining structural cost, conditional rule cost, and imperfect fit. Within it, for $M$ disjoint groups of size $k$, the clique projection's edge list is asymptotically $k-1$ times longer than the hyperedge list it replaces: the projection encodes the same grouping at higher cost. Examples from diffusion, Boolean dynamics, ecology, and ambiguous projections give graph-preferred, hypergraph-preferred, and unresolved cases; for bipartite and multilayer lifts, cost, fit, and identifiability tie, and the choice turns on which entities are posited as primitive. The position is symmetric: higher-order structure should not be inferred from phenomenology alone, nor does a graph's ability to emulate a system make it the most parsimonious or adequate description.

Conventional ferroelectrics exhibit well-defined polarization states linked through electric switching. In fluorite-structured ferroelectrics like hafnia, though, switching and oxygen diffusion seem to coexist, enriching the nature of ferroelectricity. Here we address the intrinsic, room-temperature switching and diffusion kinetics of hafnia ferroelectrics using machine-learning molecular dynamics. We identify two distinct switching mechanisms that are both active at realistic time scales. Critically, our simulations reveal that, because the lattice does not dissipate fast enough the heat originating from localized switching events, these two processes concatenate in an avalanche-like manner leading to oxygen conduction. Our results thus show that intrinsic switching leads to breakdown in hafnia ferroelectrics. They also suggest how this outcome might be avoided through suitably designed field pulses.