arXiv subjects

Yong Zhang

Publications and source records attributed to Yong Zhang.

At least 19 recordsLinked to original sources

arXiv2026

Neumann eigenvalues of isosceles triangles: monotonicity and asymptotics

We prove Laugesen and Siudeja's conjecture on Neumann eigenvalues of isosceles triangles. After multiplication by the squared diameter, the first positive symmetric eigenvalue increases strictly with the apex angle $θ$, while the first antisymmetric eigenvalue decreases strictly up to the equilateral triangle and increases strictly thereafter. \rev{The proof combines a slice-average estimate of directional energies with the explicit equilateral eigenfunction.} A quadratic correction across slices also gives a two-term expansion for every fixed positive spectral index $k$ as $θ\downarrow0$, with relative correction $θ^2/6$ and remainder $O_k(θ^4)$.

math.SP↗

arXiv2026

Large-Amplitude Steady Solitary Water Waves with General Vorticity

We study two-dimensional steady solitary gravity water waves with general vorticity, allowing for overhanging free-surface profiles. The main challenges arise from the free boundary, the unbounded fluid domain, and the inherent complexity of the general vorticity setting. To address these, we introduce a conformal reformulation that reduces the problem to an equivalent system on a fixed strip, consisting of an overdetermined elliptic problem coupled with an elliptic boundary-value problem. This framework enables a local analysis without imposing restrictive assumptions on the vorticity. Using the center-manifold construction of Chen, Walsh and Wheeler \cite{chennonlinearity}, we first establish the existence of small-amplitude solitary waves for such non-trivial vorticity distributions. Subsequently, via a global analytic bifurcation argument, we prove the existence of continuous branches of large-amplitude solitary waves for analytic vorticity functions. Along these global solution curves, the free surfaces may develop overhanging profiles and need not remain graphs over the horizontal coordinate. Our results provide a new constructive framework for large-amplitude solitary waves with general vorticity, extending the existing theory beyond the classical settings of constant vorticity \cite{susannaarma} and non-overhanging profiles \cite{milesjma}.

math.AP↗

arXiv2026

Global bifurcation of water-wave fronts generated by surface pressure

We study two-dimensional steady gravity water waves with general vorticity in a homogeneous, inviscid fluid of finite depth, subject to a surface pressure that tends to distinct constants upstream and downstream. Starting from a fixed supercritical shear flow, we construct two global branches of monotone fronts connecting distinct laminar states, with increasing and decreasing profiles corresponding to the two signs of the pressure transition. Small-amplitude fronts are first obtained via the implicit function theorem and then extended by analytic global continuation.

math.AP↗

arXiv2026

PACT: From Credit Assignment to Critic Alignment

Reinforcement learning has become a central component of large language model (LLM) post-training, yet token-level credit lacks a generally accepted mathematical definition, leaving its relationship to commonly used training signals unclear. We formulate three regularity conditions, namely Completeness, Prefix Consistency, and Neutrality, and prove that they uniquely determine token-level credit. This characterization provides a unified basis for explaining phenomena across existing algorithms and guides the development of an improved actor-critic training procedure. Through this lens, an ideal teacher in On-Policy Distillation (OPD) acts as an implicit critic, yielding an expected policy gradient proportional to that induced by token-level credit. Response-level REINFORCE Leave-One-Out (RLOO) signals match the expected policy-gradient contribution of token-level credit despite their coarser granularity. We further establish approximate credit sparsity under bounded outcome rewards and show how intermediate critic errors in Generalized Advantage Estimation (GAE) can become comparable to the underlying credit. These motivate Policy Aligned Critic Training (PACT), which adopts an Actor-then-Critic update order to apply importance sampling correction to critic training and better align the critic with the updated policy. In agentic mathematical reasoning, PACT achieves 72.87% average accuracy across four benchmarks, outperforming GRPO and PPO by 8.80 and 13.16 percentage points, respectively. On SWE-bench Verified, PACT achieves a pass rate of 67.4%, outperforming PPO, GRPO, and SAO by 2.4, 2.0, and 3.8 percentage points, respectively.

cs.LG↗

arXiv2026

Exact Nonperturbative Equilibrium Mode Statistics in Nonlinear Wave and Lattice Systems

We derive exact finite-size nonperturbative representations of equilibrium modal occupations and related statistics for three representative nonlinear systems: the Majda-McLaughlin-Tabak dispersive-wave model, the Fermi-Pasta-Ulam-Tsingou beta anharmonic chain, and the discrete nonlinear Schrodinger lattice field. Independent simulations confirm the predictions from weak to strong nonlinearity. For DNLS, the theory remains accurate across the weak-coupling quasicondensation crossover, where large low-mode occupations and long-range coherence amplify interaction effects even when the bare nonlinear coefficient is small. The finite-ring DNLS occupations are further resolved into a positive sum of Rayleigh-Jeans channels with distinct correlation lengths, explaining when a single Rayleigh-Jeans law applies and why it fails near quasicondensation. In MMT and DNLS, the exact occupations also determine the mean modal frequencies even when the dynamical spectra broaden or split. The nonperturbative results allow a direct assessment of two representative perturbative approaches. Treating the mean interaction appropriately yields accurate low-order approximations, including at strong nonlinearity. At higher orders, however, the corrections cease to decrease and successive approximations oscillate with increasing amplitude; both finite-order approaches also fail near weak-coupling quasicondensation. Thus neither low-order agreement nor a small bare coupling guarantees a reliable perturbative description. The results establish nonperturbative equilibrium theory for widely used nonlinear wave and lattice models and provide a quantitative basis for modal distributions of energy, particles, and optical power in nonlinear optics, dispersive waves, anharmonic lattices, and cold-atom systems.

cond-mat.stat-mech↗

arXiv2026

Rollout Efficiency in Reinforcement Learning for Reasoning Large Language Models: A Taxonomy and Future Directions

Reasoning-oriented reinforcement learning enables large language models to solve mathematical, coding, and other multi-step tasks, but shifts a substantial portion of the training cost to rollout, where trajectories are generated for policy updates. Efficient rollout mechanisms are therefore essential to reduce this cost while maintaining the freshness, consistency, and statistical validity of training data. This survey provides a systematic taxonomy of recent research on rollout efficiency for reasoning-oriented reinforcement learning, classifying existing approaches from both mechanism and bottleneck perspectives. Based on this taxonomy, we analyze how different technique families address distinct sources of rollout inefficiency, examine opportunities and potential conflicts for combining them, identify gaps in the evaluation and reporting of efficiency gains, and discuss open challenges and future research directions.

cs.AI↗

arXiv2026

The existence spectrum of near triple arrays with four rows

In the 1950s and 1960s, Agrawal introduced a class of experimental designs that later became known as triple arrays. Gordeev, Markström and Öhman proposed near triple arrays by relaxing all three intersection properties of triple arrays, allowing two values concentrated around the average intersection size, as well as two consecutive values for the replication numbers. They completely resolved the existence of near triple arrays with three rows, showing that there exists a $(3\times c,v)$-near triple array if and only if $v\geq c\geq 3$ except for $(c,v)\in\{(3,6),(4,6),(5,8)\}$. In this paper, we further investigate the existence of near triple arrays with four rows and prove that there exists a $(4\times c,v)$-near triple array if and only if $v\geq c\geq 4$ except for $(c,v)\in\{ (4,9),(5,7),(5,10),(6,8),(7,9),(10,12),(11,13)\}$.

math.CO↗

arXiv2026

Equivalence of Pseudo- and Approximate Amenability in Banach Algebras

We prove that pseudo-amenability implies approximate amenability for Banach algebras with a bounded approximate identity. Consequently, these two notions of generalized amenability are equivalent for such Banach algebras. Our proof closes a gap in the paper by F. Ghahramani and Y. Zhang, Pseudo-amenable and pseudo-contractible Banach algebras.

math.FA↗

arXiv2026

Generalized amenability in quantum groups

We study generalized amenability of locally compact quantum groups $\mathbb{G}=(\scr M, Δ, ϕ, ψ)$. Let $C_r^*(\mathbb{G})$ and $VN(\mathbb{G})$ denote, respectively, the C*-algebra and von Neumann algebra generated by the quantum left regular representation of $\mathbb{G}$. With natural covariance assumptions and a traceability condition on $VN(\mathbb{G})$, we show that if $C_r^*(\mathbb{G})$ is approximately amenable, then $\mathbb{G}$ admits an invariant quantum mean. We show further that the same conclusion holds if the predual algebra $\scr M_*$ has a bounded approximate identity and is approximately amenable.

math.OA↗

arXiv2026

Topologically protected chiral sensing using Synthetic Chiral Light

Chirality underlies molecular function in living matter, yet its optical detection remains challenging because conventional chiroptical spectroscopies rely on weak corrections to the dominant electric-dipole light-matter interaction, making desired optical signals weak and fragile. Topology offers a route to robustness, enabling observables whose defining properties survive disorder and imperfections. However, experimental realization of a practical topological observable for chiral spectroscopy has remained elusive. Here we realize chiral topological light and demonstrate such an observable. A tightly focused, phase-locked, counter-rotating two-colour field encodes chirality in the three-dimensional electric-field trajectory while its dominant topological charge resides in the longitudinal electric-field component where it remains hidden from direct far-field detection. An isotropic chiral medium acts as a topological transducer, converting the latent topology of the driving field into a propagating nonlinear response whose topological charge becomes directly observable in the far field while remaining strongly suppressed in achiral media. Using randomly oriented chiral single-crystal powders, we experimentally detect the enantio-sensitive response through the topological charge of the emitted field. Directly accessible in the far field and robust against experimental imperfections, this observable allows us to track and control chiral signal on attosecond timescales through the relative phase of the driving two-colour fields. Our results establish topology as a practical resource for ultrafast chiral optical spectroscopy.

physics.chem-ph↗

arXiv2026

From Intent to Execution Grant: An Execution-Boundary Conformance Profile for High-Risk AI Actions

AI agents increasingly propose actions with external consequences, including financial transfers, infrastructure changes, software deployments, disclosures, and physical actuation. Authorization engines, policy languages, runtime monitors, provenance mechanisms, and agent guardrails provide important foundations, but do not necessarily define a common semantic contract for the final transition from a particular candidate action to execution authority. We specify EBL-Core, an execution-boundary conformance profile for deciding whether one canonical, fully materialized AI-generated candidate may receive action-scoped execution authority under explicit conditions. It binds a structured intent object, Root and Operational Policies, evidence obligations, typed evidence, context, time, and a verifiable Decision Derivation through an Execution Release Contract (ERC). An ERC is not an authority-bearing token; a verified ALLOW ERC may support a separate Execution Grant governed by Redemption-time validation. EBL-Core specifies action binding, policy non-weakening, evidence handling, deterministic adjudication, derivation verification, and grant lifecycle behavior. An accompanying reference artifact provides schemas, adjudication, separate verification and Semantic Replay, and a linearizable in-memory grant store. In the retained run, 34 static vectors and 15 lifecycle checks matched expected outcomes. Across 100 trials, 32 concurrent Redemption attempts yielded exactly one successful Redemption and protected test effect per trial; 100 Revoke-Redeem races ended in valid terminal outcomes. These bounded results demonstrate executability of the specified subset, not human-intent correctness, evidence truth, complete mediation, production readiness, mechanized correctness, or deployment-level security.

cs.CR↗

arXiv2026

Fermionic hidden zeros

We uncover and prove a general class of hidden zeros in tree-level amplitudes with massless fermions. For arbitrary even numbers and arbitrary arrangements of massless real adjoint fermions and gluons, color-ordered gauge-theory amplitudes in $D=4,6,10$ vanish on general rectangular kinematic loci supplemented by species-dependent bridge conditions. The fermion--fermion bridge is governed simply by the vector current $χ_iγ^μχ_j$, while mixed and gluonic bridges are fixed by the corresponding gauge-covariant contractions. A worldsheet analysis proves the result at arbitrary multiplicity and traces its universality to the local fusion channels $ff\to g$, $fg/gf\to f$, and $gg\to g$, with no new primitive bridge structures appearing at higher fermion multiplicity. The same mechanism extends to ten-dimensional amplitudes with gravitons and arbitrary even numbers of gravitinos in factorized gamma-traceless polarizations, and to single-trace Einstein-Yang-Mills amplitudes with adjoint gluinos and gravitons. These results expose a finite local structure underlying fermionic hidden zeros across gauge and gravitational amplitudes.

hep-th↗

arXiv2026

Algebraic and Topological Study of Bell States and Quantum Teleportation

Bell states and quantum teleportation play crucial roles in quantum information and computation. However, a comprehensive theoretical study of both topics remains to be carried out. This work aims to investigate key algebraic properties of generalized Bell states and explore the topological features of quantum teleportation. First, the basis theorem and the basis group are introduced to show that the extension of a generalized Bell basis by a unitary matrix still forms an orthonormal basis. Then, a twist operator is defined to establish a connection between a generalized multi-qubit Bell state and a tensor product of two-qubit Bell states. In addition, the Temperley--Lieb algebra, the braid group relations, and the Yang--Baxter equation are employed to provide a topological description of generalized Bell states and quantum teleportation. The results demonstrate that our approach not only offers a clear illustration of relevant quantum information protocols but also reveals the topological nature of quantum entanglement and teleportation.

quant-ph↗

arXiv2026

Physics-Informed Error Field Learning: A Post-Training Optimization Framework for Physics-Informed Neural Networks

Physics-Informed Neural Networks (PINNs) have emerged as an important class of numerical methods for solving partial differential equations (PDEs). However, during the late-stage optimization process, further parameter updates often yield diminishing accuracy improvements while increasing computational costs. To address this issue, this paper proposes a Physics-Informed Error Field Learning (PIEFL) framework for PINNs. Unlike conventional approaches that continuously approximate the solution field using a single network, PIEFL introduces an auxiliary error network after the primary network achieves satisfactory accuracy and shifts the learning objective from the solution field to the error field. By deriving error control equations under physical constraints, the error network learns the discrepancy between the current approximation and the exact solution, and the learned error correction is combined with the primary prediction to improve solution accuracy. The proposed framework avoids continuous optimization of the entire solution space and focuses computational resources on correcting existing prediction errors. Moreover, PIEFL requires no modification to the primary network architecture, making it compatible with existing PINN models and applicable as a general post-training optimization strategy. Numerical experiments on representative PDEs demonstrate that PIEFL achieves higher solution accuracy under the same computational budget, validating its effectiveness in improving the performance of PINNs.

cs.LG↗

arXiv2026

The Complexity of Minimizing Subsidies in Envy-Free House Allocation

The house allocation problem is a classical one-sided matching problem that concerns the assignment of a set of $m$ houses to $n$ agents according to their preferences, where each agent is assigned exactly one house. Among the various objectives studied in this setting, envy-freeness is one of the most widely adopted fairness criteria. As envy-free house allocations do not always exist, we address this challenge by introducing subsidies and aim to compute allocations that achieve envy-freeness with minimum total subsidy. For binary instances, we show that a total subsidy of at most $(n-1)$ suffices to guarantee envy-freeness in house allocation, and this bound is tight. Building on the known NP-hardness for general utilities, we further show that computing an allocation that minimizes the total subsidy is NP-hard, even under binary utilities. However, when there are only a bounded number of types of agents with binary utilities, the problem can be solved in polynomial time. Finally, we present a polynomial time algorithm that computes the minimum subsidy required to achieve envy-freeness for two types of agents with general utilities.

cs.GT↗

arXiv2026

Multi-stage neural operator learning with application for convolutions

Convolution integrals widely exist in applications, and to enable fast and accurate computations, this paper introduces two general multi-stage neural operator learning frameworks. The first, Deep Collocation Neural Operator (DCNO), is a supervised approach that iteratively refines the operator approximation by learning residuals from input-output data pairs. The second, Deep Galerkin Neural Operator (DGNO), is an unsupervised framework applicable when the target operator can be represented by a PDE, leveraging the weak form of the PDE residual for training. Both methods progressively construct basis operators through multiple training stages to enrich the approximation space, leading to significantly improved accuracy over standard one-shot operator learning. We provide theoretical analysis for their approximation capabilities and implement them for learning convolutions. Extensive numerical experiments demonstrate that both DCNO and DGNO achieve high accuracy, approaching machine precision under single float for convolution problems, and offer substantial efficiency gains for numerous queries or parametric variations compared to traditional solvers. We also extend these frameworks to handle multi-input operator learning scenarios involving variations in both the density and kernel of a convolution.

cs.LG↗

arXiv2026

Who Can Make the Action Happen? An Authority-Decomposition Framework for High-Risk Automated Systems

High-risk automated systems distribute control across services, credentials, protected components, and lifecycle mechanisms. Labels such as authorized, approved, privileged, or protected therefore do not answer a basic causal question: which actors can actually make a consequential action occur? This paper provides an action-relative method for deriving which trust-domain coalitions are sufficient to cause protected execution, defined as the occurrence of a designated protected state transition. The framework models components, powers, resources, boundaries, and alternative realization structures; includes update, recovery, override, disablement, and alternative invocation; and separates causal control over execution from control over the authoritative account of an operation. It derives inclusion-minimal sufficient coalitions and tests whether claimed execution boundaries remain independent of designated upstream domains. Cross-domain analytical cases illustrate the method. In a split-control, release-intended, open-state, source-bounded Havenlon protocol model, the ordinary witness requires five trust domains, while certificate replacement yields a three-domain inclusion-minimal known requirement set among source-enumerated protocol witnesses; the Linux domain remains insufficient for the complete transition. Deployed global non-bypassability and boundary-bound veto coverage remain unresolved. The framework is a conceptual and analytical tool. It does not certify implementations, establish deployment security, guarantee complete discovery of hidden powers, or define evidence-verification semantics.

cs.CR↗

arXiv2026

PDRs4All XXII. Near-Infrared continuum in the Orion Bar

Conspicuous excess emission is present in the near-infrared (NIR) region in various objects, including reflection nebulae, planetary nebulae, and nearby galaxies. However, the spatial distribution and spectral shape of the excess emission remain poorly understood. We studied the NIR continuum emission spectroscopically and obtained its spatial distribution relative to the aromatic infrared band (AIB) at 3.3um in the Orion Bar prototypical photodissociation region (PDR). We aim to characterize its spectral shape and discuss its origin. We employed 3D spectroscopic data of the Orion Bar taken with the integrated field unit of NIRSpec on JWST from the Early Release Science program "PDRs4All." Contribution from the foreground ionized gas was estimated using the Cloudy code and subtracted. The observed regions were divided into nine physically distinct regions and an average spectrum was derived for each region. The nine regions, including the ionized gas, atomic PDR, and molecular PDR, clearly show remaining continuum in the region 1--4.5um. The continuum at wavelengths longer than 2.7um shows good correlations with the 3.3um AIB, while the correlation of the continuum at 1.2um is not significant. We further find that the NIR continuum in the Orion Bar can be approximated by a summation of two blackbodies. The low-temperature component correlates with the AIB well, while the high-temperature component does not. The average spectra also show absorption features at 3.0 and 4.27um, which are attributed to the presence in the spectra of water ice and CO2 ice. We discuss possible origins of the NIR continuum, among which recurrent fluorescence from carbon clusters better explains the observed low-temperature component. The presence of ice species suggests a contribution from a deeper layer of the PDR along the line of sight producing characteristic ice absorption features.

astro-ph.GA↗