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arXiv2026

Limit distribution of algebraic integral points on curves

For a quasi-projective arithmetic surface $\mathcal U/\mathbb Z$ and a compact subset $E\subset \mathcal U(\mathbb C)$ under mild regularity assumptions, we study algebraic integral points on $\mathcal U$ whose Galois orbits lie in $E$. We characterize the collections of local probability measures that arise simultaneously as the local limit distributions of Galois orbits of such points. Our result also works for measures prescribed at a subset of places. This generalizes the results of Smith and Orloski--Sardari on $\mathcal{U}=\mathbb{A}^1$ concerning the archimedean place. As a consequence, we prove an integral version of Szachniewicz's theorem on curves, which states that every \emph{integral} GVF functional can be approximated by a sequence of algebraic integral points in the GVF topology. We also give several applications: we prove that the essential minimum of height functions on curves can be attained by algebraic integral points; we connect integer Chebyshev constants with the essential minima of certain height functions on $\mathbb{A}^1$ and prove a conjecture of Montgomery; we also answer affirmatively a question of Levenberg--Londhe by showing that the smallest limit of averaged trace of totally positive algebraic integers can be attained by a sequence of totally positive algebraic units.

math.NT↗

arXiv2026

Nonperturbative Dyson--Schwinger equations in QCD: a first approximation

We consider a procedure for nonperturbative quantization based on an infinite system of nonperturbative Dyson--Schwinger equations. We propose a first approximation for truncating this infinite system of equations in the static case. The main ideas underlying this approximation are as follows: (a) the two-point Green's functions of vacuum gauge fields are factorized by introducing scalar fields; (b) in the non-vacuum case, the degrees of freedom of the $SU(3)$ gauge field can be divided into ``almost classical'' and ``almost quantum'' degrees of freedom; (c) the four-point Green's functions of the gauge fields are represented as bilinear combinations of two-point Green's functions; (d) an approximation for the three-point Green's function describing the interaction between quarks and gauge fields is proposed, which leads to the splitting of the original Dirac equation for the quark-field operators into two equations, one describing the expectation value of the fermion field and the other acquiring a nonlinear term and serving to describe a condensate composed of sea quarks bound by the vacuum gauge field. We consider the choice of gauge appropriate for this approximation to nonperturbative quantization. We point out that the emergence of a nonlinear Dirac equation within this approximation may lead to a mass gap in the energy spectrum of solutions of the corresponding systems of equations. The issue of the emergence of ``dimensional transmutation'' within this approximation is also discussed. We provide arguments in favor of the statement that the ``closure constants'' appearing in the finite truncation and giving rise to ``dimensional transmutation'' should survive in the transition to the infinite system of Dyson--Schwinger equations. An analogy between nonperturbative quantization and the stochastic theory of turbulence is also discussed.

hep-th↗

arXiv2026

LIBERO-Agent: Evaluating General-Purpose Agents for Direct Embodied Manipulation

General-purpose agents can plan, use tools, and revise their behavior from feedback, but it remains unclear whether these capabilities transfer from digital environments to embodied manipulation. To investigate this question, we introduce LIBERO-Agent, an agent-native benchmark for evaluating these agents in robot manipulation tasks. Rather than asking agents to submit task-level Python control programs or operate through high-level robot skills, LIBERO-Agent provides an interactive robotic environment where agents can select which observations to inspect, process them with their own tools, and issue native action commands. LIBERO-Agent integrates 200 tasks into a common interaction framework and provides a 30-task primary suite that separates perception, short-horizon execution, and long-horizon composition. Results reveal a pronounced reliability gap: while agents perform well on perception and easy short-horizon tasks, their performance degrades substantially on hard short-horizon and long-horizon tasks. Richer observations improve short-horizon manipulation, while demonstration benefits depend on the agent and format. Among these agents, GPT-6 Astra achieves the strongest overall performance. Further analysis shows its major advantage lies in mechanism interaction, especially when sustained physical contact is needed, while its remaining failures stem from cross-stage interference and geometric errors.

cs.RO↗

arXiv2026

Hamilton-connected cores and five cycle--wheel Ramsey numbers

Let $W_s=K_1+C_{s-1}$ denote the wheel on $s$ vertices. We give structural proofs that $R(C_{14},W_{11})=27$ and $R(C_{15},W_{11})=29$. Together with the theorem of Chen et al. for $n\ge16$, these equalities give $R(C_n,W_{11})=2n-1$ for every $n\ge14$. The two boundary values were included in an earlier survey announcement. We also give structural proofs of $R(C_8,W_7)=15$, $R(C_9,W_7)=17$, and $R(C_8,W_9)=15$. The common starting point is a Hamilton-connected core lemma. For the eleven-vertex wheel, bounds on vertex connectivity and on the matching number of a bipartite graph associated with a local cycle yield a vertex cut of order nine. Paths with prescribed endpoints then rule out every possible pair of orders of the two remaining vertex sets. For the smaller wheels, we use the structure of critical cycle colorings and local cycle-shortening arguments. We also give complete structural classifications of the $(C_8,C_6)$- and $(C_9,C_6)$-critical colorings, recovering the previously reported counts 24 and 26. All proofs are combinatorial and use no exhaustive graph enumeration.

math.CO↗

arXiv2026

A new characterization of the hazard rate and reversed hazard rate orders with applications

We propose a general characterization of the hazard rate and reversed hazard rate stochastic orders for random variables that are absolutely continuous with respect to a common dominating measure. This framework is useful in giving a unified treatment of continuous, discrete, and mixed distributions without requiring ad hoc approximation techniques or restrictive integrability assumptions. Using this result, we provide direct proofs of the bivariate characterizations of both orders. Additionally, we introduce the class of $\overline{G}$-IFR and $\overline{G}$-DRHR distributions on additive groups, unifying aging properties across different domains and proving their closure under convolution. Finally, we revisit and extend the classic results of Shanthikumar and Yao (1991) on the preservation of hazard rate orders under random sums, simplifying the underlying conditions and accommodating discrete and mixed sum components.

math.PR↗

arXiv2026

Rotating bases for finite element exterior calculus: closed-form change of basis under vertex permutations

The geometrically decomposed bases of the polynomial differential form spaces $\mathcal{P}_rΛ^1$ and $\mathcal{P}_r^-Λ^1$ on a simplex are products of a barycentric scalar polynomial and a directional or Whitney 1-form. These bases depend on an ordering of the simplex vertices. On unstructured meshes, neighbouring cells need not agree on this ordering, making it non-trivial to achieve conformity in finite element software. Existing strategies compute degree-of-freedom transformation matrices numerically, or impose a global vertex ordering through face-bubble spaces or by preprocessing the mesh. We consider the standard basis of the $\mathcal{P}_r^-Λ^1$ (trimmed) space and introduce a new basis for the $\mathcal{P}_rΛ^1$ (full) space, for arbitrary polynomial order $r \geq 1$ and dimension $D \geq 2$, and prescribe their basis polynomials as shape functions. We show that the pullback of shape functions under the change of coordinates induced by an arbitrary vertex relabelling $π$ in the symmetric group $S_{D+1}$ admits a closed-form, combinatorial expression. For most basis functions this pullback is a single basis function of the relabelled ordering, up to sign. On an explicitly characterised "filter-hit" set, this pullback is a signed sum of at most $D$ (full space) or exactly two (trimmed space) relabelled basis functions. All coefficients are in $\{-1, +1\}$ for all $r$, $D$ and $π$. The inverse transformation is obtained by computing the formulas at $π^{-1}$, so no numerical inversion of a change-of-basis matrix is needed. Conforming assembly and evaluation on simplicial meshes with arbitrary vertex orderings reduce to index manipulation. Our results are compared with the study of relabelling-invariant bases of Berchenko-Kogan and Licht, and verified in an open-source Julia implementation in the Gridap.jl library.

math.NA↗

arXiv2026

Can Domain Generalization be Guaranteed in Small-Sample Learning?

The small-sample learning problem remains a fundamental challenge in machine learning because limited training data lead to unstable model estimation and generalization. Structural Risk Minimization (SRM) has long been regarded as a principled solution under the classical i.i.d. assumption. However, domain generalization (DG) violates this assumption, leaving the theoretical role of SRM in DG largely unexplored. To bridge this gap, we establish the first theoretical guarantees for SRM in DG under mild assumptions. Specifically, based on the concept of stability, we derive learning consistency and generalization error bounds and prove that these bounds become tight when the hypotheses satisfy the stability condition. Building upon this, under a specific hypothesis space assumption, we establish stability, learning, and generalization bounds for SRM. We further discuss the applicability of these bounds to deep learning. This work establishes theoretical foundations for SRM under distribution shifts and sheds light on the design of robust DG algorithms in small-sample scenarios.

cs.LG↗

arXiv2026

From Knowledge to Legitimacy: A Philosophical Problem Discovery of AI Implementation Readiness in Public Health Disease Surveillance

Despite being an emerging credible means of using artificial intelligence (AI) for improving disease surveillance via early detection of outbreaks, epidemics prediction and evidence-based decision-making, there continue to be challenges in the use of AI tools in many low- and middle-income countries (LMICs) due to various factors including fragmented health information system, digital inequality, governance problems and institutional incapability. Most of the research conducted so far has concentrated on the efficacy and accuracy of AI in terms of predicting outbreaks, with little focus on other conditions necessary for its deployment. This study adopts a qualitative problem-discovery research design, integrating thematic analysis with philosophical analysis to examine the structural and normative barriers surrounding AI implementation in disease surveillance. The analysis identifies four interrelated dimensions of implementation readiness: epistemic adequacy, distributive justice, ethics of governance, and institutional legitimacy. These dimensions provide a framework for understanding how limitations in knowledge integration, unequal digital infrastructure, privacy and accountability concerns, and deficits in institutional and public trust can constrain the practical adoption of AI-enabled surveillance. Rather than proposing another predictive model, this study develops a theoretical framework that conceptualizes AI implementation in disease surveillance as simultaneously a socio-technical and normative process. The framework provides a foundation for subsequent empirical investigation and offers a structured perspective for designing more context-sensitive, ethically grounded, and institutionally sustainable AI-enabled disease surveillance systems in resource-constrained healthcare settings.

cs.CY↗

arXiv2026

Spike-driven Vision-Language-Action Model

Vision-language-action (VLA) models bridge multimodal understanding and robotic control, advancing the dominant paradigm for embodied intelligence. However, most existing models rely on large Transformers, whose latency and energy costs hinder deployment on resource-constrained platforms. Through sparse event-driven computation, spiking neural networks offer a promising paradigm for high-performance and energy-efficient computing. Here, we propose the first Spike-driven VLA framework enabling end-to-end direct training for robotic manipulation, which mainly comprises three core components. First, we develop spiking visual and instruction encoders for multimodal perception, encoding visual observations and language instructions into sparse, reliable spike representations for subsequent cross-modal fusion. Then, we introduce Multi-Winner Spike Fusion for instruction-guided scene understanding, using bidirectional top-$k$ winner-take-all spike routing to suppress background interference and yield fused memory. Finally, we propose a Spike Action Chunking Transformer that incorporates spiking cross-attention over the fused memory and the current robot state, enabling efficient end-to-end generation of continuous action chunks for robotic control. Extensive experiments on LIBERO and Meta-World demonstrate that Spike-driven VLA achieves competitive performance with fewer parameters and lower estimated inference energy than conventional VLA models. This work establishes a foundational framework for neuromorphic VLA modeling, paving the way for future advances in resource-efficient embodied intelligence.

cs.CL↗

arXiv2026

Probing jet quenching via the correlation of groomed jet substructure observables in Pb$-$Pb and pp collisions

A measurement of the correlation between the splitting angle $θ_{\rm g}$ and the momentum-sharing fraction $z_{\rm g}$ of the first hard splitting in a parton shower in pp collisions and 0$-$10% central Pb$-$Pb collisions at $\sqrt{s_{\rm NN}}$ = 5 TeV with the ALICE detector is reported. Charged-particle jets are reconstructed using the anti-$k_{\rm T}$ algorithm with a jet resolution parameter $R$ = 0.2, in the transverse-momentum range $60 \leq p_{\rm T,ch\;jet} < 80$ GeV/$c$. The Soft Drop grooming algorithm is used to identify the first splitting in the parton shower. Jets observed in Pb$-$Pb collisions are narrower than in pp collisions. This effect is more pronounced for balanced than for unbalanced jets. No significant modification of the momentum-sharing fraction is observed for jets with small opening angles. In contrast, there is a hint that jets with a large opening angle may be less balanced in transverse momentum in Pb$-$Pb collisions compared to pp collisions. The correlations between $θ_{\rm g}$ and $z_{\rm g}$ are well described in pp collisions by PYTHIA 8 and POWHEG while HERWIG shows too few jets with large opening angle. In Pb$-$Pb collisions the measurement is compared to a variety of models. The measurement is insensitive to the different implementations of medium response. Inclusion of elastic scatterings, as implemented in the HYBRID model is preferred to describe the unbalanced jets with large $θ_{\rm g}$ in Pb$-$Pb collisions. The balanced jets, however, are less sensitive to elastic scatterings.

nucl-ex↗

arXiv2026

Light-driven Modulation of 1-bit Metamaterial Unit Cells and Arrays

Shape-morphing materials have the potential to realise simple, tunable telecommunication arrays without the need for complex circuitry. However, existing devices either lack individual cell control, or require an integrated power supply, reducing their beamsteering ability and increasing size, weight and power consumption. This paper presents a simple, photothermally activated 1-bit reflectarray unit cell requiring no integrated power sources. The unit cell consists of dimer elements, which are connected or disconnected via a photothermally activated electrical bridge to achieve modulation. The paper discusses the shape memory materials used for switching, and presents a design for a photothermal switching mechanism. The unit cell is validated by waveguide experiments, showing strong agreement with simulations at the working frequency of 3.7GHz. Finally, a 4-cell array is created. Each cell is activated sequentially, with good agreement between simulation and experiment, demonstrating the ability to control each cell exclusively. This study therefore demonstrates that a 1-bit unit cell can be photothermally configured without complicated electronics or an integrated power supply, opening the door to a new class of shape-morphing reflectarray.

physics.app-ph↗

arXiv2026

Flexible discrete translational surfaces

We give a full list of translational nets which flex within their class of discrete surfaces of translation, by reducing the classification problem to the one of flexible complete bipartite frameworks on the sphere, for which the solution is known. We also obtained two novel classes which correspond to Bottema's spherical 16-bar mechanisms and the constant diagonal angle frameworks. Based on an algorithm for the construction of all flexible translational nets, we also discuss flexible translational tubes and toroids. Furthermore, we present novel results for both topologies which are implied by Bottema's spherical 16-bar mechanisms.

cs.CG↗

arXiv2026

Referential Uncertainty in Human--AI Collaboration

Effective human-AI collaboration requires partners to establish references through interaction, which becomes fragile when descriptions are ambiguous, similar referents compete, or partners see different things. We study referential uncertainty - uncertainty over which candidate object a description refers to - in a collaborative puzzle task where a human Helper instructs an AI Worker to place pieces. The Worker must identify and communicate its uncertainty, and the Helper must recognize and act on it. We show that a separately elicited belief distribution over candidate pieces is better calibrated (ECE 0.15) and better discriminates correct from incorrect placements (AUROC 0.65) than raw action-token probabilities, which are severely overconfident (0.97 mean confidence, ECE 0.44). Across three frontier vision-language models (GPT-4.1, GPT-5, GPT-5.5), this elicited uncertainty rises predictably with instruction vagueness, but not with competing referents in context, even when those increase errors. The models seldom externalize it, asking for clarification on only 3.5-16.7% of turns. In a controlled human study (N=210), participants given only the Worker's default message accept 78% of wrong placements and cannot tell right from wrong (AUC 0.50). Precise descriptions and, especially, well-targeted hedges cut wrong-move acceptance to 36% while largely preserving correct-move acceptance, compensating for missing shared awareness such as not seeing the Worker's action. But this benefit depends on targeting: a deployable hedge derived from the model's own belief entropy inherits that signal's weakness and can do more harm than good. Externalized uncertainty helps a human partner only when it is accurately targeted.

cs.AI↗

arXiv2026

B-GRASP: A Bayesian Framework for Inferring Graph Weights from SPDE-Inspired Dynamics

We present B-GRASP (Bayesian GRAph inference with SPDE priors), a Bayesian framework for inferring uncertain edge weights in stochastic dynamical systems on graphs from noisy observations of nodal states. The unknown edge weights parameterize the graph differential operator and therefore directly govern the evolution of the graph process. Motivated by connections between differential operators in PDEs and SPDEs and their graph counterparts, we construct stochastic graph models incorporating diffusion, reaction dynamics, and stochastic forcing. The resulting hierarchical formulation jointly represents uncertainty in the graph structure and stochastic forcing. Latent graph variables determine positive edge weights and the corresponding graph Laplacian, while latent Brownian variables represent the stochastic forcing. Conditional on these variables, the graph dynamics define a deterministic forward map from which the likelihood and posterior distribution are constructed. We characterize the posterior using maximum a posteriori estimation and the No-U-Turn Sampler, enabling both point estimation and uncertainty quantification. We demonstrate the framework on a one-dimensional inverse heat-conduction problem, stationary and nonstationary graph reaction-diffusion systems with nonlinear dynamics, and state-level COVID-19 data in the United States. The numerical results show that posterior uncertainty provides information not captured by point estimates, particularly for weakly identifiable or highly conductive edges, and enables uncertainty in both graph connectivity and stochastic forcing to be quantified within a Bayesian framework.

stat.ME↗

arXiv2026

Exclusive production of $π^+ π^-$ pairs in diffractive $γp$ and in $pp$ collisions within the tensor-pomeron approach

We discuss exclusive production of $π^+ π^-$ pairs in diffractive $γp$ and in $pp$ collisions at high energies, considering resonant ($ρ(770)$, $ω$, $f_2(1270)$) and non-resonant (Drell-Söding) contributions within the tensor-pomeron approach. For the $γp \to π^+ π^- p$ reaction, the model describes well the H1 data in the region $M_{ππ} \lesssim 1.2$ GeV. We discuss the important role of the Drell-Söding mechanism in shaping the resonance line. We also predict differential cross sections for the $pp \to pp π^+ π^-$ reaction at $\sqrt{s} = 13$ TeV where at least one proton emits a virtual photon. These findings are relevant for the central exclusive production of $π^+ π^-$ pairs in the context of ALICE, ATLAS, CMS, and LHCb measurements in hadron-hadron collisions at the LHC, especially under experimental selections using only rapidity-gap conditions. Additionally, our results are also applicable to $π^+ π^-$ production in ultraperipheral $p$A/AA collisions at the LHC and to photo- and electroproduction of $π^+ π^-$ at future electron-proton/ion colliders (EIC, LHeC).

hep-ph↗

arXiv2026

Realization of ZnSe-based Field-Effect Transistors operating at Cryogenic Temperatures as a Platform for Future Spin-Qubit Applications

The wide-bandgap compound semiconductor ZnSe is a promising host material for the realization of electron spin-qubits. Its non-degenerate conduction band and the potential for isotopic nuclear spin purification promise long spin coherence times. Key requirements for such devices include reliable electrostatic control of electrons in ZnSe and low-resistance ohmic contacts that remain functional at cryogenic temperatures. In this work, we utilize a novel Shadow Wall technique for molecular-beam epitaxy combined with in-situ deposition of Al ohmic contacts to realize normally-off ZnSe-based field-effect transistors. The devices exhibit linear output characteristics and effective gate control of the channel from room temperature down to 5 K, confirming low-resistance ohmic contacts to the undoped ZnSe channel. The drain current can be modulated by several orders of magnitude through electrostatic gating, with threshold voltages of approximately 3 V and field-effect mobilities exceeding 100 cm2/Vs over the investigated temperature range. Self-consistent Schrödinger-Poisson and drift-diffusion simulations reproduce the measured transfer characteristics and provide insight into the role of interface electrostatics in determining the channel formation and threshold voltage. These results demonstrate the potential of gated ZnSe heterostructures for future spin-qubit applications.

cond-mat.mtrl-sci↗

arXiv2026

Layer codes as quantum memories: syndrome extraction, thresholds and idle robustness

Layer codes are three-dimensional local CSS codes of check weight at most six, obtained by quasi-concatenating a CSS input code with unrotated surface code patches. What is established about them describes the code, not the circuit that measures it. In this work, we evaluate them as active memories under circuit-level noise. Doing so first requires a syndrome extraction circuit, and the junction stabilizers that couple the patches rule out borrowing a surface code patch's CNOT schedule. We present a decoder-free scheduler that constrains hook propagation first and compresses depth afterwards, generate circuits for eighteen layer codes across four input codes, and compare them with surface codes of the same distance, simulated and decoded in the same way. The circuits lose no distance to hook errors on [[4,2,2]]-input codes wherever a circuit-distance proof is affordable, and reach a lower logical error rate than those of a general-purpose scheduler for CSS codes at roughly half its CNOT depth per round. Our primary family built from a [[4,2,2]] input code reaches a circuit-level threshold of $5.06(7)\times 10^{-3}$. The layer code outperforms the surface code in terms of idle robustness: at the same distance it tolerates an interval between syndrome extraction rounds 1.7-3.0 times longer than the rotated surface code. This comes at the cost of 1.7-5.0 times more operations per unit time and approximately five times more physical qubits, both per logical qubit. Finally, we model the cost of the beyond-2D cross-plane CNOTs that the construction demands, and find that their speed matters far more than their fidelity.

quant-ph↗

arXiv2026

CIDER-FM: Foundation Models for Causal Inference from Diverse Experimental Regimes

Causal foundation models (CFMs) amortise causal inference over priors of synthetic structural causal models (SCMs), predicting the effect of an experiment on a specific variable. However, observational data alone may leave multiple causal models compatible with available evidence, while experimental data with interventions on exactly the variable of interest might be unavailable. This work studies CFMs as a method to combine finite observational and surrogate-interventional datasets in order to predict a target conditional interventional distribution (CID) more accurately than with observational data alone. We first formalise the conceptual benefits of surrogate experiments. Building on this analysis, we introduce \textsc{Foundation Models for Causal Inference from Diverse Experimental Regimes} (\emph{CIDER-FM}), a causal foundation model that uses an intervention-aware representation and hierarchical three-axis attention to exchange information across variables, samples, and experimental regimes. We evaluate CIDER-FM against a wide range of baselines across diverse synthetic graph and mechanism families, as well as on both simulated and real-world data from Causal Chambers. Our results demonstrate strong CID prediction performance and show that incorporating experimental context can improve predictions over observational data alone.

cs.LG↗