Papers

Let $\mathcal{N}^h_\Omega$ be the null ideal of the Hausdorff measure constructed by Davies and Rogers. We give a Tukey reduction of $(\mathcal{N}^h_\Omega,\mathcal{N}^h_\Omega,\subseteq)$ to a localization system with finite coordinate sets. It follows that $\mathfrak{v}^\forall_{D,g}\le\operatorname{add}(\mathcal{N}^h_\Omega)$ and $\operatorname{cof}(\mathcal{N}^h_\Omega)\le\mathfrak{c}^\forall_{D,g}$ for some $D, g \in \omega^\omega$. Consequently, we prove the consistency of $\mathfrak{d}<\operatorname{add}(\mathcal{N}^h_\Omega)$ and, separately, $\operatorname{cof}(\mathcal{N}^h_\Omega)<\mathfrak{b}$. Hence the additivity and cofinality of $\mathcal{N}^h_\Omega$ can differ from those of the Lebesgue null ideal. We also show that the finite graphs in the Davies–Rogers construction can be chosen so that $\operatorname{cov}(\mathcal{N}^h_\Omega)\le\operatorname{non}(\mathcal{N}^h_\Omega)$.

We give a negative answer to the open problem posed by Adámek and Rosický in 2001, asking whether the cocompletion of any small category under sifted colimits is finitely accessible. We will construct an infinite family of counterexamples.

Ultralight axion-like particles (ALP) are the well-motivated candidates for the dark matter. In the standard halo model, the ultralight galactic dark matter behaves as a stochastic Gaussian random field, and the polarization angle of the linearly polarized light propagating through the field stochastically oscillates proportional to the field difference between the observer and the source. The statistics of this signal depend on the source size and its distance from the observer relative to the ALP Compton length and coherence length, and therefore on the ALP mass. We present a unified statistical framework for the polarization-oscillation searches with light sources of arbitrary size and distance. We classify the statistics of the stochastic oscillation amplitude into four distinct regimes and provide a seamless description including the transitional regimes between them. Our framework reproduces the signal models in previously known cases including the laboratory-scale searches and searches using pulsars and the cosmic microwave background. We provide a likelihood prescription that incorporates the stochasticity of the signal, and show that uncertainties in source distance must be carefully accounted for, as they can alter the resulting constraints on the ALP-photon coupling by up to a factor of three. Our results provide a consistent basis for interpreting and comparing a broad range of ALP searches with astronomical polarized sources.

The frequency-dependent tidal response of a neutron star is constrained by causality, reality and passivity, which turn a suitably rescaled response into a holomorphic self-map of the upper complex frequency half-plane after some suitable conditions. The Schwarz–Pick theorem then bounds the leading dynamical correction to the tidal deformability from above. In this work we confront this bound with the most recent calculations of the dynamical tidal response in the literature which have also shown that the static tidal deformability and its correction at second order in frequency are tightly correlated. We find that the bound is saturated to within a few per cent, a quantitative confirmation of f-mode dominance in the relativistic regime. The combination of the static deformability with an independent determination of the f-mode frequency thus may provide an equation-of-state-independent upper limit on the dynamical tide.

We present the first holographic study of gravitational form factors (GFFs) of scalar, pseudoscalar and canonical-spin-averaged tensor glueball targets. These observables test gravitational cubic couplings whose physical validity is not established by spectra and static-force calibration. We construct a dynamical Einstein–scalar–axion representation inspired by the Babington–Crooks–Evans adjoint-mass deformation of $\mathcal N=4$ super-Yang–Mills theory and its Type-IIB supergravity dual. Leading ultraviolet source data are retained, while a soft-wall-like infrared reconstruction incorporates asymptotically linear radial mass-squared trajectories. Spectra and Wilson observables fix the parameters at a common Sommer scale without GFF input. The full constrained cubic vertices fail to describe 27 correlated scalar lattice observations, giving $\chi^2/\mathrm{dof}=73.60/27=2.73$. We propose normalized heavy-target (HT) effective cubic couplings for pure-glue matching. HT adopts leading radial shapes suggested by infinitely heavy targets at fixed probe dynamics and normalizes their overlap weights on the physical ground states. With the background, modes and propagators unchanged, HT gives $\chi^2/\mathrm{dof}=16.98/27=0.63$, without numerical adjustment to GFF data. Tensor and scalar source overlaps determine $A$ and the physical normalized trace; the exact finite-mass energy–momentum-tensor relation determines $D$. We predict the pseudoscalar and tensor form factors and three-target Breit pressure and shear profiles. On the reference infrared-decaying axion branch, the HT Breit mass radii are $0.276$, $0.300$ and $0.311\,\mathrm{fm}$, respectively. The results identify gravitational cubic matching as a distinct step beyond background calibration and provide a prescription for further lattice tests.

Probes are the workhorse of interpretability. If a model's hidden states predict a variable, the model is said to represent it. But a probe score has no fixed meaning. An $R^2$ of 0.6 may only reflect what the input already gives away, and the same score can mean different things on different data. We propose reading every probe score against two reference points: a floor, what a declared set of simple inputs already predicts, and a ceiling, what the full input can predict. The gap between them, the headroom, is the range in which a probe can show that a model computes something beyond the simple inputs. We prove that headroom vanishes in two ways: the target stops depending on a hidden variable the model must infer, or the input stops revealing it. We test this on transformers trained for in-context meta-analysis, which must infer the hidden heterogeneity between studies to weight them correctly, and where both reference points are known. Under distribution shift, probe scores fall and prediction error rises $12$–$15\times$, yet the model recovers a similar share of the headroom, indicating that the data lost information, not the representation. We then analyze the real models. The single-cell foundation model scGPT encodes biological variability only partially. We also revisit four influential LLM probing studies, which claim that models represent geography, the state of an Othello board, truth, and the demographics of their users. Against a floor computed from the input text alone, some of these claims hold, while others are largely explained by the text itself.

Advanced electronic packaging structures represent a key technological approach for extending Moore's Law. An electronic packaging structure consists of multiple materials with distinct properties, constituting a composite structure with complex spatial architecture. This paper develops an unfitted cut finite element method (CutFEM) for transient heat conduction simulation in multi-material electronic packaging structures with complex material interfaces. In the proposed computational framework, the heterogeneous spatial geometric features of electronic packaging structures is embedded and characterized in a regular background mesh, thereby avoiding the generation of body-fitted meshes on complicated interfaces. Interface temperature and heat-flux transmission conditions are imposed by a coefficient-weighted symmetric Nitsche formulation. In addition, a ghost-penalty stabilization controls arbitrarily small intersections between the physical materials and background meshes. Furthermore, the semi-discrete and fully-discrete numerical schemes are proposed, and an explicit energy estimate is derived in detail. Finally, two-dimensional and three-dimensional electronic packaging structures containing substrate, molding compound, die, and solder balls are designed to validate its accuracy, efficiency, and scalability in simulating challenging transient thermal problems.

The development of national policy and legal outputs toward space resource utilization across several countries accelerated after the introduction of the Artemis Accords in 2020. The announcement also further intensified the debate about the necessity of specifying a regime for using space resources on the international level. In 2021 the Legal Subcommittee of the UN Committee on the Peaceful Uses of Outer Space finally approved the establishment of its Working Group on Legal Aspects of Space Resource Activities. Therefore, this chapter builds on diplomacy under conditions of polycentric governance and aims to map the diversity of actors' ideas and interests about governance for space resource utilization on the level of the Working Group. The research process follows qualitative analysis methodology and assigns the results into the matrix of prospective alternatives for governing space resources. The available materials of the Working Group including reports and recordings, constitute the core empirical data used in the analysis.

In this paper, we investigate the synthesis of Micro Neural Policies (MNP) to enable safe and robust real-time robotic control on computationally constrained embedded devices. We demonstrate that integrating Evolution Strategy (ES) and Statistical Model Checking (SMC)-based verification for policy search can drastically reduce neural network size without compromising safety and robustness. We conduct a large-scale training and evaluation of MNP on Cartpole and Quadrotor control tasks, varying control frequencies and network architectures. After validating these policies in simulation, we evaluate their deployability through zero-shot transfer to physical systems. Our experiments show that MNP can successfully achieve safe sim-to-real transfer without sacrificing control performance. We then show that the policies' memory footprint, ranging from 0.5 to 7.5 kB, allows deployment on microcontrollers, where they achieve real-time inference latency with under 25 ns of jitter while leaving the chip idle for over 97% of the time for additional workloads. This makes them a highly practical solution for severely resource-constrained robotic systems.

Whether alignment gets easier or harder as models grow is often argued from isolated findings, as if alignment were one property. We treat it as a family of measurable scaling relations: for each risk category r, the alignment burden needed to hold a fixed safety target is modeled as B_r(N)=a_rN^alpha_r, with N a capability proxy; against a budget proportional to N, scaling helps if alpha_r<1, keeps pace if alpha_r~1, and accumulates alignment debt if alpha_r>1. We give three operationalizations of burden and distinguish observed, audited and true alignment. A toy model, in which corrections consume capability headroom, makes the consequences explicit. We prove that the largest exponent among corrected risks, not an average, sets the long-run regime; that above 1 any policy holding headroom above a floor must grow super-exponentially; that, for burdens that are positive mixtures of power laws, fits on small models underestimate large-scale exponents; and that an audit that uncovers hidden failures without false positives never underestimates true alignment. We propose a pre-registrable protocol and apply reduced versions of it twice. A preregistered reanalysis of public adversarial-training data for Pythia classifiers finds that the compute needed to bring attack success under 10% grows as N^0.60. A preregistered pilot on Qwen2.5 0.5B-72B finds exponents of -0.05 for truthfulness and 0.48 for stated dispositions (both scaling helps under its reduced rule, though local slopes approach 1 at the top; replicated on Qwen3 0.6B-14B), while sycophancy (0.89, or 0.83 with two seeds added at 72B) and a planted backdoor are undetermined: the backdoor is removed quickly when its trigger is known but survives blind safety training at four of five sizes. We release four browser games that play these laws (www.aisafety.fun). We make no claim about which regime holds for current frontier models.

Remote sensing scene classification is a fundamental task in Earth observation and geospatial analysis. Existing approaches mainly follow three paradigms: task-specific visual classification, vision-language similarity matching, and autoregressive multimodal generation. However, visual classifiers rely on predefined label spaces, CLIP-based methods perform recognition through static image-text alignment, and multimodal large language models (MLLMs) introduce unnecessary token-level generation for classification tasks with explicit candidate categories. To address these limitations, we propose RSJEV, a one-pass multimodal decision framework for remote sensing scene classification. Unlike conventional MLLMs that formulate classification as autoregressive text generation, RSJEV reformulates scene classification as a candidate-conditioned multimodal discriminative decision process, where visual representations, task instructions, and candidate category semantics are jointly modeled. Specifically, we introduce a OnePass Decider that extracts multimodal decision states and directly estimates category probabilities within the candidate category space, eliminating autoregressive decoding while preserving vision-language interactions. Extensive experiments on three widely used remote sensing scene classification benchmarks, including UC Merced, AID, and NWPU-RESISC45, demonstrate that RSJEV achieves superior classification performance compared with representative CNN-, Transformer-, Mamba-, CLIP-, and MLLM-based methods. Moreover, RSJEV significantly reduces inference costs and achieves a better accuracy-efficiency trade-off with only a compact 0.8B-parameter model. These results demonstrate the effectiveness of state-conditioned multimodal decision making for efficient remote sensing image understanding. The code will be available at https://github.com/Dongtcs/RSJEV.

Probabilistic load forecasting has been widely studied for power-system operation and planning, but customer- and transformer-level forecasting introduces a distinct scalability challenge. At these levels, load uncertainty is strongly affected by customer behavior, weather, and mixed load composition, making it difficult for a single shared model to capture heterogeneous patterns. Using separate probabilistic models can improve local accuracy, but becomes costly to train, store, update, and validate at scale. To address this challenge, we develop a scalable customer-aware forecasting framework that learns common demand behavior through a shared model while adapting only a compact subset of parameters. Rather than using an independent model for each load or assigning each load to a specialized model, the proposed design learns a small bank of low-dimensional adaptation components and allows each load to combine them according to its forecasting characteristics. This preserves shared knowledge across customers while providing sufficient flexibility for heterogeneous and mixed load compositions. Experiments on 590 load profiles from the SMART-DS dataset show consistent improvements in deterministic accuracy and probabilistic quality over statistical, neural-network, Transformer-based, and pretrained time-series baselines, while retaining low storage and inference costs.

In the field of Explainable AI (XAI), counterfactual (CF) explanations interpret a model's decision by suggesting the changes to the input that would lead to a more favourable outcome. To be useful in practice, such an explanation should change few features and change them as little as possible, properties known as sparsity and proximity. We observe that existing methods remain limited in this respect, especially for numerical features, whether they are model-agnostic and amortised, or gradient-based with full access to the model. In this paper, we propose FlowCF, a model-agnostic generative method that frames CF generation as sparse transport from the factual to the target class. We solve this transport with flow matching, which we extend to mixed feature types with a novel mixed flow operator, and exploit the resulting geometry to optimise for sparsity through a gating network that minimises the number of features the transport changes. Extensive experiments on six benchmark datasets demonstrate that FlowCF produces the best numerical sparsity and proximity, changing 29% of the numerical features where the best baseline changes 89%, at 70% smaller displacement, while remaining comparable on the other desiderata.

Conductive metal-organic frameworks (c-MOFs) are promising electronic materials, where electronic states critically determine electrical conductivity. However, achieving controllable modulation of these states during crystallization remains challenging. Existing approaches rely either on redesigning framework components or on introducing external dopants after crystallization, making electronic-state regulation dependent on structural modification or postsynthetic doping. Here, we demonstrate a crystallization-enabled in situ proton-management strategy for regulating the electronic state of c-MOFs. Using Co9HHTP4 as a model system, we show that distinct proton environments influence the balance between competing proton-coupled electron-transfer pathways during Co-O framework assembly while preserving the fundamental framework architecture. HNO3-mediated crystallization produces an electronic state consistent with enhanced electron retention within the Co-O framework and results in a single-crystal conductivity of 8.4 * 10-2 S cm-1, nearly four orders of magnitude higher than Co9HHTP4-NaOAc (1.7 * 10-5 S cm-1), together with a substantially reduced transport activation energy. Hall measurements further reveal a pronounced increase in carrier concentration for Co9HHTP4-HNO3, providing direct evidence that the enhanced conductivity is associated with a substantially increased carrier population. These results establish crystallization conditions as an active parameter for programming electronic states and charge transport in conductive frameworks.

Coulomb friction is a non-associated law: it contains a threshold that depends on the contact pressure, i.e. a stress that is not conjugate to any internal variable, hence it admits no dissipation potential in the sense of generalized standard materials (GSM), and the incremental frictional contact problem is not a minimization problem. In this paper, we propose an alternative friction model that retains Coulomb-like behavior while being associated and fully GSM-compatible. Key to our formulation is the introduction of a new internal variable motivated by the microscopic contact state of rough surfaces, whose evolution is driven by the plastic deformation of the asperities. Under a non-decreasing contact pressure and below a threshold pressure, the model recovers Coulomb friction up to an asperity-scale penetration depth. This depth is physically meaningful and can be calibrated to reproduce known tribology results. Under decreasing contact pressures, the model exhibits a memory effect due to irreversible plastic deformation of the asperities, whereas above the pressure threshold it yields a saturation of the frictional traction. We present both penalty and Lagrange multiplier formulations of the model. A 2D finite element implementation of the penalty approach confirms excellent agreement with the classical Coulomb predictions across two benchmark tests.

Understanding the principles behind Shampoo has recently guided the development of more effective neural network optimizers. These methods learn a preconditioner by optimizing the Frobenius or Kullback-Leibler (KL) divergence against the gradient second moment. In this work, we investigate how the choice of divergence shapes preconditioning, which remains unclear and blocks further improvements. To do so, we develop a unified Bregman divergence framework that connects all popular divergences, allowing us to study them jointly. Through empirical spectral analysis of gradient second moments, we examine how divergence choice shapes Kronecker approximation and interacts with finite-sample error in preconditioning. We find that some divergences can better compensate for finite-sample underestimation of the empirical second moment, helping explain the differing behavior of their corresponding Shampoo variants. We further validate this explanation through GPT-2 pretraining experiments. By connecting divergence choice to practical training behavior, we believe our framework provides principled guidance for understanding the foundations of, and further improving, Shampoo.

Geometric alignment scores based on Gram determinants provide a compact way to model higher-order consistency among modalities, yet how such scores respond to modality degradation is poorly understood. This paper asks whether the response of a multimodal geometric score is determined primarily by the magnitude of the perturbation-induced displacement. Using frozen cohorts from MSR-VTT (N=878) and DiDeMo (N=980), we apply controlled video blur and audio noise and analyze the response in the relational geometry on which the score is defined. Displacement magnitude explains at most 15% of the out-of-sample variance in the absolute response, and magnitude-matched pairs respond systematically differently, so scalar magnitude does not organize the response. The closed-form first-order expansion of the Gramian volume yields the Directional Geometric Response (DGR): the projection of the displacement onto the local volume gradient, which jointly captures the clean operating point, displacement magnitude, and displacement direction. The absolute first-order DGR term explains the observed response with out-of-sample R^2 of 0.838-0.969, matched-magnitude ranking accuracies of 0.864-0.963, and response-sign accuracies of 0.909-0.989, whereas the tested direction-free alternatives remain weak or unstable under the corresponding evaluation protocols. A pre-specified gain-normalization candidate, V/(g_V+eps), fails its predictability and clean-order gates. DGR uses the observed degraded-state displacement and is therefore an explanatory quantity, not a deployment-time predictor: geometric response depends on where the representation operates, how far degradation moves the relational geometry, and in which direction it moves.

Trajectory optimization (TO) under nonlinear dynamics, actuation limits and collision avoidance constraints is a fundamental problem in robotics, albeit especially challenging due to its highly non-convex nature. For this setting, Differential Dynamic Programming (DDP) is an efficient second-order shooting method, yet its local structure renders it vulnerable to suboptimal basins. Sampling-augmented variants mitigate this susceptibility through stochastic exploration, but often sample only around the few trajectories they retain for reoptimization, based solely on their cost which restricts exploration breadth. We introduce Pareto-Optimal Entropy-Regularized DDP (PER-DDP), an entropy-regularized population framework derived from the free-energy/relative-entropy inequality. Our method combines prior-guided sampling that shapes exploration around each retained trajectory, with expanded rollout evaluations that probe these sampling policies beyond the few retained candidates, and Pareto filtering for preserving task-constraint alternatives across iterations. This decouples sampling effort from the optimization population size and broadens exploration without sacrificing the second-order structure that makes DDP effective. Across multiple systems and hundreds of environments, PER-DDP achieves higher success rates than state-of-the-art sampling-augmented TO methods and finds reliable solutions in environments beyond the reach of all baselines.

Transitional millisecond pulsars are often identified through X-ray light-curve morphology, especially by visual comparison with the prototype PSR J1023+0038. Such classifications remain qualitative and lack a calibrated notion of how much variability is already present within the prototype itself. We introduce a Dynamic Time Warping (DTW) framework that compares light curves through moving-window similarity distributions and calibrates candidate-prototype distances against the internal heterogeneity of PSR J1023+0038. In this formulation, a source is not simply asked to resemble one prototype observation, but to remain compatible with the range of morphologies exhibited by the prototype across observations. We apply the method to confirmed and candidate tMSPs and to a control sample of non-tMSP systems. The resulting similarity measure provides a reproducible ranking for tMSP-like behaviour and is therefore useful for candidate triage and archival searches. At the same time, the control sample shows that short-timescale accretion variability can partly mimic tMSP-like morphology, demonstrating that light-curve shape alone is a screening diagnostic rather than a definitive class identifier.

Classical theories of heat conduction in magnetized plasma predict that thermal transport, mediated by Coulomb collisions of electrons, occurs predominantly along magnetic field lines. Recent theoretical and computational studies challenge this description for weakly collisional, magnetized plasmas in which thermal pressure dominates magnetic pressure (so-called high-e̱ta} plasmas). Such plasmas, which include the intracluster medium of galaxy clusters and inertial-confinement-fusion hot spots, are thought to be susceptible to kinetic-scale microinstabilities that can suppress parallel heat conduction. Revised theories of heat conduction accounting for these instabilities have been proposed, but experimental data with which to benchmark them are lacking. Here, we report experiments at the Orion laser facility in which the temporal evolution of temperature of a high-e̱ta}, weakly collisional plasma is sensitive primarily to the thermal conductivity along its initially quasi-laminar magnetic field. We characterize the temperature, density and magnetic field using x-ray spectroscopy and imaging, and proton imaging. Once stochastic magnetic fluctuations develop, the measured temperature evolution requires suppression of thermal conduction by at least an order of magnitude relative to classical predictions, providing the first laboratory evidence linking magnetic microturbulence with suppression of heat conduction in a high-e̱ta} plasma.

We propose G-EXO, an inverse-designed intrastromal corneal exoskeleton for keratoconus. Unlike conventional intracorneal ring approaches, G-EXO is conceived as a patient-customizable, sectorial and anisotropic scaffold whose geometry and stiffness are optimized to redistribute corneal deformation and reduce asymmetric optical aberrations. We develop a three-dimensional finite-element screening model with localized ectatic weakening, physiological intraocular pressure, and an intrastromal reinforcement domain. A representative design produced a modest but consistent reduction in pressure-induced coma, with a mesh-refined estimate of about 5%, while displacement and stress metrics were more numerically stable. The study is presented as a computational feasibility framework rather than a clinical validation. Its main contribution is to formulate intrastromal reinforcement as a free-form optical-biomechanical inverse-design problem. Patient-specific tomography, nonlinear anisotropic corneal mechanics, full optical modeling, and ex-vivo validation are identified as the next steps.

Clinical diagnosis is inherently a structured reasoning process, yet existing deep learning models often bypass this structure by mapping image features directly to disease labels without explicitly interrogating the morphological and textural criteria that clinicians systematically evaluate. This limits diagnostic transparency and may compromise safe clinical deployment. We present MedCORE (Medical Criteria-Oriented Reasoning and Evidence), a structured diagnostic framework that operationalizes clinical reasoning within a vision-language architecture. For each input image, MedCORE decomposes the diagnostic process into clinically defined criteria, spatially localizes each criterion to diagnostically relevant image regions, encodes evidence through multi-scale representations that capture macro-structural and micro-textural pathological characteristics, and refines criterion representations using a Graph Attention Network that explicitly models inter-criteria dependencies. Criterion representations are further aligned with clinical text descriptors, reinforced through class-wise visual prototypes, and aggregated using uncertainty-calibrated weighting that proportionally discounts low-confidence diagnostic evidence. MedCORE is validated across three clinically heterogeneous imaging modalities, including dermoscopic lesion classification on ISIC 2018, breast ultrasound lesion characterization on BUSI, and diabetic retinopathy grading on IDRiD. Quantitatively, MedCORE achieves 89.2% accuracy, 85.7% macro-F1, and 96.4% AUC on ISIC 2018; 96.1% accuracy, 95.2% macro-F1, and 98.4% AUC on BUSI; and 84.3% accuracy, 80.2% macro-F1, and 92.8% AUC on IDRiD. These results demonstrate consistent improvements over strong CNN, transformer, biomedical vision-language, concept-based, and prototype-based baselines.

Hybrid architectures combining linear sequence models with softmax attention provide an effective balance between efficient long-context modeling and precise token retrieval. Existing designs such as Native Hybrid Attention (NHA) combine compressed long-term states with sliding-window attention, but their exact attention is restricted to a fixed local window. In this work, we introduce Prefix-State Hybrid Block Attention (PHBA), which replaces local sliding-window attention with top-k block-sparse retrieval and couples each retrieved block with a compact prefix state summarizing its preceding context. The prefix states are constructed by a gated linear recurrence at block boundaries and retrieved together with the corresponding token blocks, allowing the model to combine precise long-range evidence with compressed historical context within a unified layer. We further develop a hardware-aware Triton implementation that streams routed token blocks and prefix states without materializing large intermediate tensors. Experiments show that PHBA improves long-context and retrieval performance over strong linear and hybrid baselines while retaining efficient training and inference.

Vision-Language-Action (VLA) models have achieved impressive results in robotic manipulation and ground-mobile navigation, yet language-conditioned control of unmanned aerial vehicles (UAVs) in smart warehouses remains largely unexplored, hindered by the lack of benchmarks that jointly provide continuous low-level flight actions, fine-grained natural-language target descriptions, and realistic industrial environments. This paper introduces WareFly-VLA, a photorealistic UAV VLA framework and dataset for language-guided human search, localization, and tracking in warehouse environments. It contains 507 human-teleoperated flight episodes and 8,504 high-resolution RGB transitions collected in NVIDIA Isaac Sim, each paired with a human-written appearance description of the target worker and a synchronized four-degree-of-freedom control command. Two aerial tasks are covered: target approach and person following, under occlusion, long-range search, altitude variation, and clutter. A unified benchmark of four open-source VLA architectures (SmolVLA, GR00T N1.7, pi_0 and OpenVLA) is established under a leakage-free episode-level protocol at two control rates. The results show that language-conditioned aerial control in warehouses is far from solved: performance drops substantially under strict generalization settings, continuous action modeling consistently outperforms discrete action tokenization, only the forward channel is reliably learnable from a single frame, and current foundation-model interfaces transfer poorly from ground and humanoid embodiments to aerial platforms. The synchronized video, language, action, pose, and difficulty annotations further support world-model research. The dataset, baselines, and evaluation protocol are released to support language-grounded aerial autonomy in smart warehouses.

Ambiguity measures the number of accepting runs in nondeterministic finite automata (NFA). We consider finitely ambiguous NFA, where there exists a constant $N$ such that over every word $w$ there are at most $N$ accepting runs. In such a case we also say that the NFA is $N$-ambiguous. Importantly $N$ depends only on the NFA, it does not depend on the length of the word. Weber and Seidl showed that every NFA is $N$-ambiguous for $N = 2^{O(n \log n)}$, where $n$ is the number of states. We improve this to $N = 2^{O(n)}$, which is asymptotically tight.

Automated Guided Vehicle (AGV) fleets in production and logistics environments rely on a system-wide emergency stop to handle local anomalies such as malfunctions, hazards, or contaminated areas. While safe, this approach halts the entire fleet even when only a small area is affected, causing unnecessary downtime. This paper proposes dead zones — a formally defined localized isolation approach that serves as an additional fail-operational mechanism for situations where a full system-wide halt is not strictly needed. Rather than shutting down the entire fleet, a dead zone isolates the anomalous area, allowing unaffected robots to continue operating normally. We introduce two operational strategies: basic dead zone handling, in which affected robots enter a dead zone and stop, and dead zone handling with escaping, in which robots that are sufficiently far from a dead zone reroute around it. For escaping on counterclockwise trajectories we prove collision-freedom with a bounded arrival delay for all escaping robots, provided a minimum pairwise separation is kept between robots. Experimental evaluation confirms the theoretical guarantees and characterizes the throughput tradeoffs between all three approaches: full emergency stop, basic dead zone handling, and dead zone handling with escaping.

Dissolved oxygen is important for the ocean's ecosystems and biogeochemical cycles. Yet, Earth System Models (ESMs) vary in their simulations of the present-day and future ocean oxygen inventory. To narrow down the uncertainty in estimates of ocean oxygen content, we train a conditional generative diffusion model on outputs of a multi-model ESM ensemble to learn the conditional distribution of upper-ocean oxygen given physical input variables such as temperature and salinity. This generative model has considerable skill in the Atlantic and Southern Oceans, and can generate realistic oxygen samples under conditions not seen in the training data. We validate this model using observational datasets, and use it to generate oxygen fields for models without oxygen data using only temperature and salinity as conditioning inputs. This physics-conditioned extrapolation suggests that model biases in the tropical Pacific Oxygen Minimum Zone may be smaller than currently assumed when considering a larger set of physical ocean states. Our approach provides a complementary way to represent probabilistic multi-model climate distributions.

In colloids, anisotropy in either shape or particle interactions can steer assemblies away from close-packed monolayers and towards more intricate structures. In this study we utilize both shape and interaction anisotropy to stabilize porous surface assemblies of triblock elliptical particles, whose surfaces are decorated with two attractive patches at opposite poles. The resulting structures display a tunable degree of crystalline kagome order, controlled by quenching the temperature and/or changing the chemical potential. In particular, we find evidence that nucleation into the kagome lattice proceeds via a one-step pathway, in contrast to the two-step route widely reported in spherical triblock systems, making triblock ellipses an interesting model system for studying how self-assembly pathways change with particle shape. Beyond ordered crystalline structures, we find disordered porous networks with complex internal geometry. To characterize this range of assemblies, we introduce a particle-patch graph that explicitly captures the localization of bonds at distinct patches. Bonding motifs follow directly from this representation, while the loops, that we identify as the pore boundaries, can be determined from the graph's planar embedding. We detect all loops as the face boundaries in the planar embedding by means of a face-walking algorithm, distinct from shortest-path approaches used in ring detection. Together with a new local and global order parameter measuring the loop network's regularity with respect to a selected loop size, this framework connects microscopic bonding motifs to mesoscopic pore properties and quantifies the tunable order of these porous assemblies.

Whether the spin-1/2 Aharonov-Bohm Hamiltonian supports bound states has remained controversial since Hagen concluded that no such states exist for a Dirac particle. Here, we show that Hagen's solution corresponds to a particular member of the one-parameter family of self-adjoint extensions that describe the singular Zeeman interaction, and we identify which member the microscopic physics selects. Matching the extension parameter to a finite-radius flux tube yields $\nu=0$ precisely at $g=2$, and it does so in every flux sector. The critical $g$ factor is therefore universal, $g_c=2$, and depends on neither the flux sector nor the regularization radius. The flux sector controls the depth of the bound state energy, and we obtain a closed-form expression showing that binding deepens markedly with the integer part of the flux. Hagen's conclusion is thus confirmed and sharpened: it is not a statement about one arbitrary member of a family of extensions, but about the member that the physics selects when the magnetic moment takes its Dirac value, and an anomalous moment is a necessary and sufficient condition for binding in the singular channel.

The Fock representation of the unscreened Coulomb interaction, a block of separable terms with analytic form factors and strengths, is included in the momentum-space Faddeev kernel of three-body bound states beside the separable nuclear terms. A bound-state kernel evaluates every pair interaction at negative pair energies, where the representation is exact and convergent, so the Coulomb force enters without a screening radius and without a limiting procedure. With this representation the $^{3}$H–$^{3}$He splitting of the CD~Bonn potential is in very good agreement with the exact Faddeev result; in the $S$-wave model space the Coulomb-distorted form factors give about half the Fock value. The Feshbach–Schur projection of the Pauli-forbidden states acts on the forbidden eigenstates of the nuclear-plus-Coulomb pair Hamiltonian, the Coulomb-dressed states obtained inside the extended separable problem, as the eigenstate condition requires. The Coulomb displacements of the cluster-model states of $^{6}$Li, $^{9}$Be and $^{12}$C and of the $^{9}$Be–$^{9}$B mirror pair are given. The eigenstate condition is tested in $^{9}$Be and $^{12}$C by replacing the Coulomb-dressed forbidden states with those of the Coulomb-subtracted interaction and with the oscillator functions of the orthogonality-condition model.