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At least 1,513 records · Page 84Linked to original sources

A special Hardy estimate in the axisymmetric swirl problem

We examine the proof of Dongyi Wei's logarithmic circulation criterion. A trace estimate specific to $\nabla(u_r/r)$ replaces a generic squared-swirl form bound by one with one logarithm rather than two. Repeating the coupled $J$--$Ω$ energy and comparison argument then gives a proposed threshold of order $(\log D)^{-5/4}$. Under the hypotheses stated below, the proof is intended to establish regularity when $|r u_θ|\le C|\log r|^{-α}$ uniformly near the axis with $α>5/4$, and at $α=5/4$ with an absolute sufficiently small coefficient. Every analytic step, including the cutoff core and exterior terms, is included for independent checking.

math.AP↗

Conservative Meta-Agent Search: Architecture Adaptation under Non-Stationarity

Automated agentic-system design is typically evaluated on static task suites with immediate scalar rewards. Deployed systems face persistent shift, delayed dependent feedback, correlated component failures, and costly architecture changes. We formalize meta-agent architecture search as sequential incumbent replacement with switching costs and hard risk constraints and introduce Conservative Meta-Agent Search (CMAS). CMAS retrieves archived architectures and proposes typed graph edits, then scores each against the incumbent by paired shadow replay under common random numbers, with interventional component credit. Promotion requires an empirically calibrated, variance-penalized simultaneous score above a pre-specified margin, and is followed by a simulated canary stage and pre-specified rollback. Since backtests cannot certify meta-level skill, we introduce MetaInvest-Bench, a regime-switching simulator whose specified worker competence makes a surrogate-optimal architecture computable, with leakage-controlled replay, adversarial governance tracks, and five negative controls. Financial streams serve as a risk-sensitive testbed for meta-level generalization; we claim no alpha. Across 96 streams, CMAS cuts normalized mean surrogate dynamic-oracle regret from 0.116 to 0.104 and raises held-out utility from 0.44 to 0.48 over the strongest adaptive baseline; when extra workers add no value, it contracts to near-single-agent teams. Its deployment inference cost is ~6% lower, though its search-inclusive token cost is the highest of the methods compared. The observed per-update false-promotion rate is 3.4% against a nominal 5% target, and 4.8% in a sealed rerun. The calibration is empirical: it concerns an update-level replay statistic on an author-designed benchmark, and guarantees neither full-utility improvement, nor absence of simulated canary-stage harm, nor sequence-level error control.

cs.AI↗

Homomorphic Encryption with Coset Code Construction

Homomorphic encryption enables computation on input data without decrypting it. This paper extends a construction based on scalar message codes, utilizing coset codes to pack $k$ message symbols into a ciphertext vector of length $n$. For a given field and vector length, this packing method reduces the number of ciphertext vectors required to transmit a message record. A compatible family of evaluation codes supports public addition and multiplication operations up to a predetermined degree. We prove that the scheme achieves bounded chosen-plaintext security under the coordinate-label distinguishability assumption.

cs.IT↗

DIAL: Steerable Language Models with Distilled Instruction-Adherence Levels

When a user says "Keep it short", how short should the LLM's response be? More generally, users and applications require different levels of instruction adherence, but prompting does not reliably provide fine-grained control over them. We therefore study "steerable language models" that provide fine-grained numerical control over the degree to which models follow general instructions specified in text. However, existing approaches do not jointly offer fine-grained control, efficiency, and scalability across diverse instructions. To address this gap, we introduce DIAL (Distilled Instruction-Adherence Levels) to achieve all three properties. For fine-grained control, we perform classifier-free guidance (CFG) with a frozen LLM to provide training signals for on-policy distillation of instruction adherence at different levels. For efficiency, we design a lightweight steering adapter that uses a classifier over the LLM's hidden states to compute a closed-form steering edit. The classifier adaptively sets the steering magnitude at each token based on the target adherence level, while accounting for the geometry of the LLM's hidden states to preserve response coherence. For scalability, the classifier is text-conditioned, allowing a shared adapter to support new instructions without per-instruction fitting, and training requires only instruction and request text. Evaluation across multiple LLM families shows that DIAL achieves a competitive balance between concept expression and response fluency, with concept scores increasing monotonically across adherence levels. We introduce SteerIF, an instruction-only dataset of 98, 625 concept, persona, verifiable, and descriptive instructions. When trained on SteerIF, DIAL provides fine-grained control over personas and, when combined with prompting, improves verifiable instruction following.

cs.AI↗

Multi-Token Prediction and Alternative Tokenization Improve Learning Latent Multi-Hop Graph Search at Scale

Given an unseen graph, a start node, $s$, and an end node, $t$, can a language model generate the shortest path from $s$ to $t$? Prior work has found that models fail to learn this task as the graphs scale. We show that this failure has two causes: the supervision signal and the tokenization. First, we theoretically establish and empirically demonstrate the effectiveness of multi-token prediction (MTP), and show that the benefits of MTP are topologically agnostic. Second, we introduce alternative tokenizations and show that the two causes are orthogonal. Using these methods, we break through the scaling wall observed by prior work, consistently and stably learning to solve the task at scales far beyond previous limits.

cs.LG↗

Random Survivor Sets with Moving Holes in Bedford-McMullen Carpets

Let $2\le m < n$ be integers, and let $K(\mathcal{A})$ be the Bedford--McMullen carpet generated by $\{(x,y)\mapsto((x+i)/m,(y+j)/n):(i,j)\in\mathcal{A}\}$, where $\mathcal{A}$ is a subset of $\{0,1,\ldots,m-1\}\times\{0,1,\ldots,n-1\}$. Write $\mathcal{B}$ for the set of occupied columns, and assume that $\#\mathcal{B}\ge2$ and each column contains at least two symbols of $\mathcal{A}$. At each vertex of the column tree $\mathcal{B}^*$, we independently choose one forbidden symbol from $\mathcal{A}$ according to a prescribed distribution. Let $\mathbb{P}$ denote the resulting product measure on $\mathcal{A}^{\mathcal{B}^*}$. This gives a random survivor set $K_ω(\mathcal{A})$ with $ω\in\mathcal{A}^{\mathcal{B}^*}$. We show that, for $\mathbb{P}$-a.e. $ω$, \begin{equation*} \dim_H K_ω(\mathcal{A})=\frac{1}{\log m}\log\left(\int \sum_{b\in\mathcal{B}}\ell_b(ω)^{\frac{\log m}{\log n}} d\mathbb{P}(ω)\right), \end{equation*} where $\ell_b(ω)$ is the number of surviving symbols in column $b$ at the root.

math.DS↗

Gravitational Wave Diffractive Images Reveal the Structure of Astrophysical Objects

Scattering patterns encode the structure of extended objects, as demonstrated by charged particle scattering on atomic nuclei. Gravitational wave (GW) diffraction offers an analogous probe of otherwise invisible mass distributions. At linear order in the lens potential we derive expressions relating the central diffractive image contribution to a gravitationally lensed GW waveform to the Fourier transform of the projected lens density. For finite mass lenses this contribution takes the form of a point mass Born amplitude multiplied by a normalized mass form factor, analogous to that in nuclear scattering. As the frequency of GWs from a merging compact binary source evolves the signal samples this form factor across spatial scales, imprinting lens structure through interference with the primary image. Using full numerical wave optics calculations we quantify the observational reach for extended dark matter objects, primordial black holes halo-dressed by dark matter halos and superradiance clouds of ultralight bosons around black holes. For the considered source populations, five year observations with next generation detectors can distinguish extended lenses from point masses, probing dark matter fractions down to $\mathcal{O}(10^{-5})$, and halo-dressed primordial black holes from matched bare black holes, probing primordial black hole dark matter fractions down to $\mathcal{O}(10^{-6})$. For sufficiently close source-lens configurations, scalar superradiance clouds can produce distinguishable diffraction signatures for boson masses of approximately $10^{-17}-10^{-12}~\mathrm{eV}$. These results provide a framework for characterizing extended dark matter and compact object astrophysical environments.

astro-ph.CO↗

Local heights for nef toric compactified divisors

We present a definition of a local height of nef toric divisors in the sense of Yuan and Zhang by approximating a height for canonical divisors and then using the local energy to extend to other metrics on the same geometric divisor.

math.AG↗

ConQEC: Concolic Testing for Quantum Error-Correcting Code Implementations

Quantum error-correcting code (QECC) implementations are hybrid software-control systems: measured syndromes drive decoder dispatch, recovery actions, and logical checks. Existing QECC verification techniques can prove formal obligations, and general quantum testing can expose final failures, but developers still lack a scalable testing workflow that generates concrete faults and explains where a QECC repair path first diverges. This paper presents ConQEC, to our knowledge the first concolic testing framework for QECC implementations. By combining concrete (Pauli) fault replay with symbolic repair-path constraints, ConQEC generates tests that expose not only final logical failures but also fault--syndrome--decoder--recovery (FSDR) diagnostics: the injected fault, observed syndrome, decoder decision, recovery action, oracle result, and earliest divergent stage. Its symbolic encoding of Pauli faults, syndrome predicates, decoder and recovery relations, and oracle checks enables this diagnostic workflow to scale beyond exponentially increasing amplitude-level quantum-state reasoning. We implemented ConQEC and evaluated it on generated source-level QECC families and public QECC artifacts with up to thousands of qubits. ConQEC detects the seeded bug in every experimental case and reports a replay-valid, fault-localizing FSDR witness for each.

quant-ph↗

Procrustes-Bering-Sheaft: Automated Model Discovery and Virtual Crash Tests for Microservices

Procrustes-Bering-Sheaft automates lightweight model discovery and virtual crash tests for microservices. Each test estimates operation availability by Monte Carlo sampling of service and communication failures. Procrustes checks deployment and tracing evidence; Bering discovers dependencies and incorporates replica declarations; Sheaft evaluates declared operation-success conditions. Independent command-line interfaces exchange reusable, versioned artifacts. The toolchain extends an earlier graph-based approach with mandatory-call contracts, failure-tolerance sweeps, baseline comparison, component-importance analysis, and CI/CD gates. We demonstrate the workflow on one HTTP operation. Six controlled execution states exposed two mismatches between reachability and observed success; an explicit required-call predicate matched all six. Two modelled one-replica additions produced different decisions: recommendation retained an availability-target violation, whereas catalog restored the baseline estimate of 0.979900 and grid tolerance of 0.12. Analytical oracles and controlled tests verify the implementation; archived replay checks numerical continuity with two earlier studies.

cs.SE↗

Boundary regularity of $k$-Hessian eigenfunctions

We prove smoothness up to the boundary for $k$-Hessian eigenfunctions on smooth bounded uniformly convex domains when $2\leq k<n$. This resolves an open problem in the regularity theory of degenerate fully nonlinear elliptic equations and extends the boundary smoothness theorem for Monge--Ampère eigenfunctions. In contrast to the Monge--Ampère case, the linearized $k$-Hessian operator remains uniformly elliptic up to the boundary.

math.AP↗

When Is a Memory Safe Enough to Act On? Action-Conditioned Verification for Long-Lived Agents

Long-lived agents act on memory carried across sessions, and many of their actions are irreversible, so a stale memory can turn directly into harm. Existing work improves the memory itself --- retrieving, refreshing, or reconciling entries --- yet whether an entry must be re-checked before acting is not a property of the entry: the same remembered address can be used unchecked for a routine shipment but should be re-confirmed before a valuable one. We therefore study \emph{action-conditioned memory verification}: given a candidate action, decide which of its memory premises to re-verify and when to proceed or abstain, balancing execution risk, abstention, and verification cost. We formulate this as a sequential stopping problem, in which a verification is worth its cost only if it can change what the agent does next; under suitable verifier reliability and cost conditions, increasing action consequence can move the same memory through proceed, verify, and direct-abstention regimes. Building on this formulation, \textsc{AMV-Guard} is a practical verification gate that extracts the premises a candidate action rests on, calibrates beliefs about whether they are wrong, and selects checks by bounded value of information (VOI). On ToolSandbox, relative to a static policy given the same inputs, it lowers mean verification cost by 33.9\% while keeping 100\% safe-proceed recall and 0\% Gate harmful, and raises Proceed coverage from 38.83\% to 44.17\%; in a gate-core transfer to AppWorld, which carries over the stopping/VOI core but not the full structured pipeline, it lowers verification cost by 21.3\% at a small cost in safe-proceed recall and task success. These results suggest that verification effort should be set by what an agent is about to do, not only by how reliable a memory appears.

cs.MA↗

Peak-Aware One-Way Trading: Competitive and Learning-Augmented Algorithms for Energy Procurement

We introduce peak-aware one-way trading ($\texttt{PA-OWT}$), an online problem in which a player must purchase a fixed quantity of an asset by a deadline, minimizing its total cost plus a charge proportional to the largest single purchase at any time. The model is motivated by electricity procurement, where the cost of energy rewards buying at low prices, but peak demand charges discourage concentrating purchases in short periods. Balancing these incentives is challenging when future prices are unknown: a large purchase can establish a peak that later decisions cannot undo. We develop a peak-aware online algorithm that balances price and peak control with deadline feasibility and achieves the order-optimal competitive ratio. We further extend our results to a learning-augmented algorithm that uses predictions of optimal purchasing decisions to achieve an order-optimal consistency-robustness tradeoff, exploiting accurate advice while retaining worst-case guarantees in the face of arbitrary prediction errors. Finally, we evaluate our algorithms in a case study on electricity procurement using historical electricity price traces to understand the benefits of peak-aware purchasing.

cs.DS↗

Semi-strict 4-categories as enriched categories

We introduce several flavours of semi-strict 4-category as enriched categories. We give the axioms for semi-strict 4-categories in elementary terms and describe a wide range of examples. In particular, we answer the question of what exactly Gray-categories and the higher transformations between them form: namely, a left-sharp 4-category G-Cat$^4$. In addition, we describe examples arising from braided monoidal 2-categories, monoidal Gray-categories (herein defined) and Gray-categories with structure. We use the concepts introduced here and the relationships between them to unify various concepts in the literature, such as Crans' 4-teisi. In the second part of the paper, we investigate homotopical aspects. In particular, we classify the equivalence n-cells in the left-sharp 4-category G-Cat$^4$ for each n. Using this, we show that the left-sharp skew monoidal structure on the category of Gray-categories induces a symmetric monoidal closed structure on the homotopy category of Gray-categories.

math.CT↗

Concentration inequalities for vector-valued martingales

In this paper, we establish several deviation inequalities for the norms of vector-valued martingales, achieving bounds of the same quality as those available in the classical one-dimensional setting. Our results extend and refine previous work by Pinelis (1994) and Hayes (2005) in this area.

math.PR↗

Simulation-based inference of profile evolution for high-precision pulsar timing

Pulsars are exceptional cosmic laboratories, the most stable of which rival atomic clocks. Nearly all of that precision rests on one observable, the average pulse profile unique to each pulsar and stable over decades. These profiles change shape systematically with observing frequency, reflecting the physics of the emitting pulsar beam, but if left unmodelled, it can bias the arrival-time measurements, undermining precision timing. Profile-domain timing has been proposed to address this effect, but current implementations use stochastic sampling, which is computationally prohibitive and has limited the application in large-scale analyses. Here, we present a simulation-based inference approach to profile-domain timing, using a normalising flow conditioned on a convolutional embedding of the frequency-phase portrait. From a single portrait, it returns joint posteriors on dispersion measures, arrival times, and the parameters governing profile evolution instantaneously, with uncertainties verified against known inputs following an initial training run. The value of a likelihood-free approach is that the simulator becomes the interface to pulsar properties. Fundamental properties like non-Gaussian noise, pulsar self-noise, jitter, scattering, and profile change can be inferred by simulating them rather than by deriving a new likelihood for each, opening a promising pathway to include machine learning methods into pulsar timing workflows.

astro-ph.IM↗

A Fast Algorithm for Quaternion Tensor Singular Value Decomposition under the T-product

Quaternion tensor singular value decomposition (T-SVD) under the T-product provides a framework for analyzing multidimensional quaternion data. However, the T-SVD construction of Pan and Ng (SIAM J. Matrix Anal. Appl., 2024) \cite{PanNg2024} contains a structural gap: an unrestricted quaternion matrix SVD need not preserve the paired Fourier block structure required for tensor factor recovery, potentially leading to loss of T-unitarity and inaccurate reconstruction. To address this issue, we develop a structure-preserving construction that transforms each paired quaternion block into a complex matrix and maps its complex SVD factors back to quaternion factors with the required structure. This construction corrects the proof of \cite[Theorem 4]{PanNg2024} and leads to a corrected version of \cite[Algorithm 2]{PanNg2024}, hereafter referred to as the ``corrected algorithm'', ensuring T-unitary tensor factors and an f-diagonal core for arbitrary third-order quaternion tensors. A numerical counterexample demonstrates the failure of \cite[Algorithm 2]{PanNg2024} and verifies the corrected algorithm at machine precision. Notably, we propose a fast structure-preserving algorithm, Algorithm~\ref{alg:t-fast}, and compare it numerically with the corrected algorithm. The experimental results show that Algorithm~\ref{alg:t-fast} reduces the decomposition time while maintaining near-machine-precision accuracy. Furthermore, its application to color video encryption yields high reconstruction quality, favorable ciphertext statistics, and stability under input perturbations.

math.NA↗

Nanopillar metasurfaces uniting high optical reflectivity with ultracoherent nanomechanics

Mechanically compliant mirrors are key components in cavity optomechanics. However, the requirements to achieve the best optical and mechanical performance are usually in direct competition. A high reflectivity for tightly focused beams entails thick reflectors, whereas ultracoherent flexural nanomechanics necessitates thin membranes. We eliminate this trade-off by introducing high-refractive-index nanopillar metasurfaces on top of a thin membrane. We pattern a 50 micrometer-diameter array of nanopillars to form a photonic crystal. The flat band behavior of guided resonances in the photonic crystal enables a reflectivity of 99.82(1)% for a tightly focused beam of 7 micrometer waist. The combination of two guided resonances creates a 100 nanometer-wide high-reflectivity band around 1550 nanometer. Simultaneously, the nanopillar patterning realizes a density-modulated phononic crystal that isolates an ultracoherent localized mechanical mode with a $Q\cdot f$-product of $2\cdot 10^{14}$Hz. The demonstrated nanopillar metasurfaces enable lightweight mirrors for room-temperature quantum optomechanics and for use as levitated mirrors or lightsails.

physics.optics↗