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arXiv2026

Extension of MDS Codes over Finite Fields

In this paper, we investigate extending of $[n,k,n-k+1]$ non-Reed--Solomon(non-RS) MDS codes to $[n+1,k,n-k+2]$ non-RS MDS codes. We develop a practical iterative algorithm for constructing longer MDS codes while preserving their non-RS structure. The proposed algorithm is inspired by the meet-in-the-middle algorithm in cryptanalysis. On average, it requires at most $O(kq^k)$ multiplications, compared with $O\left(\binom{n}{k-1} q^{k-1} k^3\right)$ multiplications for generic exhaustive search. Applying the proposed algorithm to several known families of MDS codes, including elliptic-curve, twisted Reed--Solomon, column-twisted Reed--Solomon, cyclic, and missing-monomial MDS codes over fields of order at most $32$, we obtain new MDS codes of increased lengths that remain inequivalent to Reed--Solomon codes. In particular, we construct $[9,4,6]$ codes over $\F_9$ and $\F_{13}$, each with Schur-square dimension $9$. Over $\F_{17}$, we obtain two inequivalent $[10,4,7]$ codes with Schur-square dimensions $9$ and $10$, respectively. The latter is the dual of an extended $[10,6,5]$ code, demonstrating that the method also applies when $k>n/2$. For these dimension-four codes, the Schur-square dimensions $9$ and $10$ exceed both that of RS code (Schur-square dimension $7$) and those of specific elliptic-curve and column-twisted Reed--Solomon families (Schur-square dimension $8$). Some of these parameters of non-RS MDS codes have not been reported before.

cs.IT↗

arXiv2026

NN-Based Transistor Modeling for Ultra-Fast SPICE Simulation and Standard Cell Library Characterization

Neural network (NN)-based transistor models have proven to be a promising solution to accelerate device modeling. Although these models demonstrated remarkable speedup in circuit simulations, they were not rigorously tested in complex tasks within standard EDA tool flows for chip design, which require very high transistor model precision to provide accurate results and converge properly. To investigate their full potential and promise, we develop NN-based transistor models that accurately predict the drain current and various charges for a 3nm nanosheet, and employ the models for a standard cell library characterization. This enables us to evaluate the accuracy and speedup under a very wide range of SPICE simulations, benchmarking our models against an industry-standard implementation. Since standard cell library characterization involves thousands of SPICE simulations, it serves as a great benchmark for transistor model quality and consistency. To further evaluate model accuracy, we also perform analog- and digital-level simulations for various complex circuits. Our experiments reveal that NN-based models are a valid alternative to existing transistor compact models, capable of producing accurate delay and power estimates with a much higher speed and convergence time compared to the conventional Verilog-A-based industry-standard (BSIM-CMG) transistor compact model. Our NNs achieve sub-0.11% and 0.76% errors for delay and total power evaluation on a wide range of circuits, while taking up to 8 times less time during the standard cell library characterization. Additionally, we provide comprehensive information and guidance on NN accuracy, unveiling the relationship between NN size and its effect on circuit simulation precision.

cs.ET↗

arXiv2026

Bayes Factor Testing of Linear and Nonlinear Effects in Additive Gaussian Process Regression

Gaussian process regression flexibly models nonlinear relationships between predictors and an outcome variable. A central question in this modeling framework is whether each predictor affects the outcome linearly, nonlinearly, or not at all. We propose a Bayesian testing framework for this problem within additive Gaussian process regression. Each predictor is decomposed into a standardized linear component with a $g$-prior and an orthogonalized Gaussian process component capturing nonlinear structure. The latter is governed by a standardized magnitude parameter whose value zero removes the component. Local and non-local priors are considered for the standardized magnitude parameter. Bayes factors for testing the linear and nonlinear effects are computed from the fitted full model via Savage-Dickey-type identities, avoiding expensive marginal likelihood computations of many different models. To assess the accuracy of the Bayes factor estimates, the outcomes are compared to bridge sampling estimates. Simulations and empirical applications show the performance and applicability of the methodology.

stat.ME↗

arXiv2026

Data-dependent Compact Multinode Shepard Method

We introduce a data-dependent compact multinode Shepard method for the approximation of scattered multivariate data. The proposed approach extends the compact multinode Shepard operator by incorporating nonlinear, data-dependent weights inspired by the weighted essentially non-oscillatory (WENO) methodology while preserving the partition of unity structure and the locality of the approximation. The construction is based on compactly supported multinode weight functions associated with local polynomial interpolants defined on unisolvent stencils. A smoothness indicator is employed to adapt the contribution of each stencil according to the local regularity of the underlying function, thereby reducing spurious oscillations near discontinuities while retaining the optimal approximation order in smooth regions. We establish the theoretical approximation properties of the proposed operator: it achieves the order of accuracy of its linear counterpart for sufficiently smooth functions and, under an explicit indicator-separation hypothesis, the same order is retained at every covered evaluation point near a jump discontinuity. Numerical experiments for local degrees up to four illustrate the performance of the method on both smooth and non-smooth data, on scattered as well as on gridded nodes.

math.NA↗

arXiv2026

Small black hole in de Sitter as an observer

We study the Euclidean path integral around magnetically charged lukewarm black holes in four-dimensional de Sitter space. We numerically determine the full one-loop spectrum of coupled graviton and photon fluctuations and find that the phase of the partition function agrees with that of pure gravity in empty de Sitter plus a worldline observer. In the small-mass limit, certain localized eigenmodes can be effectively viewed as describing the observer's motion and have the expected eigenvalues, allowing us to reconstruct the worldline action. We further identify these modes with translational zero modes of an extremal charged black hole in asymptotically flat spacetime, lifted by de Sitter curvature.

hep-th↗

arXiv2026

Multimodal Progress-Residual Fusion for Anticipating Navigation Retreat in Robotic Flexible Endoscopy

Flexible robotic endoscopes provide access through tortuous anatomy, where friction, deformation, and wall interaction separate commanded insertion from useful distal progress. Operators interpret this mismatch and retreat to recover a navigable configuration. Recognizing the approach to that decision requires relating motor intent to distal response and the local visual scene. We introduce Multimodal Progress-Residual Fusion (MPRF), a causal model that anticipates operator retreat from commands, electromagnetic (EM) tracking, and endoscopic video. A nominal-progress model predicts the response expected in normal or successful navigation; a temporal predictor combines its EM residual with all three observed modalities. In a 150-episode colon-phantom collection, MPRF achieves 0.580 +/- 0.007 AUPRC across three seeds, compared with 0.511 for the strongest reduced-modality control. Complete multimodal histories provide the principal ranking advantage, while the residual adds an explicit intent-response representation with a small, uncertain increment over raw fusion. Analysis of frozen alarms relates warning timing to the behavioral label and explains the increase in event recall under a longer matching window. These results establish a basis for behavioral assistance during operator-controlled navigation.

cs.RO↗

arXiv2026

AERIAL: Mission-Aware LLM Selection for Language-Driven UAV Control in Flying Networks

Unmanned Aerial Vehicles (UAVs) in Flying Networks (FNs) increasingly require mechanisms to translate high-level natural language objectives into executable missions. Although Large Language Models (LLMs) have demonstrated the feasibility of language-driven UAV control, existing approaches typically rely on static model configurations and overlook mission-aware performance variability. This paper presents AERIAL, a benchmark-driven framework for adaptive LLM selection in hybrid edge-cloud UAV control. AERIAL separates systematic model benchmarking from mission execution, deriving empirical scenario-model mappings and applying them at runtime for mission-aware selection. Evaluation across 720 automated simulation runs spanning navigation, spatial reasoning, and algorithm invocation revealed significant performance variability depending on scenario-model pairing. A case study integrating AERIAL with a FNs placement algorithm further validated the framework's ability to interface with domain-specific optimization modules through natural language. These results validate the effectiveness of AERIAL's adaptive model selection in improving reliability and operational robustness for autonomous UAV control in FNs.

cs.NI↗

arXiv2026

What Does AI Success Look Like? A Mixed-Methods Analysis of Supranational AI Governance Instruments

In the last decade and in particular since 2018, supranational institutions have published policies, guidelines, and most recently regulations to govern development and use of Artificial Intelligence (AI). This paper aims to investigate the themes and dimensions of ``AI success'' set forth by instruments of AI governance issued by supranational bodies. To this end, we use a mixed-methods approach, combining manual thematic analysis and automated topic modelling approaches, to analyse a curated corpus of 13 documents issued by supranational bodies, including the European Union bodies, OECD, G20, UNESCO, United Nations, and the Council of Europe between 2018-2025. Based on the analysis and through the lens of sociology of expectations, we propose a novel categorisation scheme for AI success themes emerging from supranational bodies' documents. Drawing on the findings, we advance a set of policy recommendations, setting forward the need to move beyond high-level principles toward more coordinated approaches to AI governance.

cs.CY↗

arXiv2026

Contact Renormalization of One-Mode Electron Correlation: Validation in Four- and Ten-Electron Systems

A stationary many-electron eigenstate has one dynamical phase although its internal response can be strongly multimode. We ask whether the stationary Hartree--Fock information carrier contains enough information to determine the scalar correlation energy through one effective return. In regularized Hartree--Fock, Gaussian primitive products fix a minimum-information relative-coordinate mode before any one-mode reduction; virial completion defines the correlation source, while exact contact measures the additional return restriction created by neighboring occupied pairs. The Be-like $1s^22s^2$ sequence establishes the one-valence-pair boundary: with no neighboring occupied valence pair, the source returns through the universal floor $D_0=\sqrt{1+δ^2}$. Ten-electron molecules and Ne-like ions then test how finite-pair contact dresses that return. The same parameter-free source--return construction reproduces the established molecular and ionic correlation trends with quantitative accuracy. The numerical agreement therefore serves as validation of a physical separation between source strength and return restriction, rather than as the objective by itself.

cond-mat.supr-con↗

arXiv2026

Parameter Constraints on $f(R^{1+ε},T_{μν}T^{μν})$ Gravity from Exotic Compact Objects

According to General Relativity (GR), gravity is described as the curvature of spacetime caused by mass and energy. Although GR has been highly successful in describing gravitational phenomena, exotic compact objects with high mass and strong gravitational fields, as well as low-mass objects, have motivated the study of modified theories of gravity. One of the modified gravity frameworks is $f(R,T^2) = R^{1 + ε} + ακ^2 T_{μν} T^{μν}$, which provides an extension of GR by introducing modifications to both the geometric and matter sectors. In this study, we investigate the mass-radius structure, physical viability, and stability of quark stars in $f(R,T^2)$ gravity using the MIT Bag Model equation of state. We compare results from the exact $f(R,T^2)$ model, its first-order Taylor expansion, and GR. The values of the gravity parameter $ε$ and $α$ are constrained by evaluating the ability of the model to reproduce the observed mass-radius configurations of compact objects, including HESS J1731-347 with a mass of $M = 0.77_{-0.17}^{+0.20} \, M_{\odot}$ and a radius of $R = 10.4_{-0.78}^{+0.86}$ km, GW190814 with a mass of $M = 2.6 \, M_{\odot}$, PSR J1614-2230, with a mass of $M = 1.928 \pm 0.017 \, M_{\odot}$ and a radius of $R > 10$ km, and PSR J0437-4715, with a mass of $M = 1.418 \pm 0.037 \, M_{\odot}$ and a radius of $R = 11.36_{-0.63}^{+0.95}$ km. We assess the physical viability and stability of the stellar configurations using the energy conditions (strong, weak, null, and dominant) and the speed of sound. Overall, the $f(R,T^2)$ gravity model can accommodate quark star configurations and reproduce the observed properties of massive compact objects, particularly those associated with GW190814 and the lightest compact object observed, HESS J1731-347, respectively.

gr-qc↗

arXiv2026

Dirac Structures and Reduction of Optimal Control Problems with Symmetries

We study the symmetry reduction of optimal control problems using Dirac structures. The first-order conditions of the Pontryagin Maximum Principle are written as an implicit Dirac system on the Pontryagin bundle. For a problem invariant under a Lie group, we reduce both the Lagrange-Pontryagin variational principle and the underlying Dirac structure, and prove that they yield the same reduced equations, which we identify with the Hamiltonian equations on the dual of the Atiyah algebroid. Reconstruction, independence of the principal connection, and the relation between criticality and optimality complete the picture. Dropping regularity, we give the Gotay-Nester-Hinds constraint algorithm a Dirac-geometric form and prove that symmetry reduction commutes with it. For control-linear systems whose admissible directions are horizontal for a principal connection, abnormal extremals lie on the leaf where the base costate vanishes, and the first secondary constraint is the degeneracy of the curvature pairing. We also give a reduced criterion for strict abnormality and a metric-free index form. Examples: a spacecraft with rotors (flat connection), the Heisenberg group (nowhere-zero curvature) and the Martinet problem (curvature vanishing on a hypersurface).

math-ph↗

arXiv2026

CANNBot-CAKE: Collaborative Agentic Kernel Evolution for Ascend NPU

Efficient custom operators are essential for modern deep learning workloads, yet developing high-performance kernels for Ascend NPUs remains slow, expert-intensive, and difficult to automate. Although AI agents now approach expert performance on GPU kernel benchmarks, current models remain less capable of generating AscendC kernels for NPUs, potentially reflecting the relative scarcity of relevant training data. We thus present CAKE, a CANN-native system for deployable custom operators that combines adaptive multi-DSL routing, separate Generation and Evolution modes, and reviewed knowledge reuse through CAKE Book and a Self-Evolving Agent. On 53 CANN-Bench v1.1 operators on Ascend 950PR, CAKE's aggregated results achieve $100\%$ case pass rate on the standard set (1,060/1,060) and $98.28\%$ on the hidden set (4,167/4,240), with an overall mean score of 78.63 out of 100 and an average performance speedup of $1.334\times$ over the baseline. Evolution then pushes correct operators further: EngramGateFusion cuts aggregate device time by $46.6\%$ over 20 rounds and roughly halves the mean roofline gap. These results offer a practical path toward closing Ascend's AI-for-kernel capability gap.

cs.AI↗

arXiv2026

The subcritical accelerating Schwarzschild-Bertotti-Robinson family

We identify the general finite-$\ell$ neutral Alekseev--Astorino Schwarzschild--Bertotti--Robinson family with the subcritical branch of the independently obtained accelerating Schwarzschild--Bertotti--Robinson solution. The exact scale-free dictionary is \begin{equation*} B^2M^2=\frac{m^2}{b^2+\ell^2},\qquad AM=\frac{m\ell}{b^2+\ell^2},\qquad \frac{A}{B}=\frac{\ell}{\sqrt{b^2+\ell^2}}, \end{equation*} up to the north--south orientation convention. Thus finite real $\ell$ covers precisely the acceleration interval $|A|<|B|$: for $\ell\ne0$ the corresponding OP acceleration parameter is nonzero and the two axial openings are unequal, although no acceleration horizon is present. We establish the identification by canonical Weyl-rod matching and horizon-shape comparison, an independent conicity check, and an exact off-horizon reconstruction of the metric and Maxwell field. The centered limit $\ell=0$ is the nonaccelerating Schwarzschild--BR solution, whereas $|\ell|\to\infty$ approaches the critical boundary $|A/B|=1$ from below. The Astorino parameter $\ell$ therefore parametrizes subcritical acceleration rather than an additional independent neutral black-hole degree of freedom.

gr-qc↗

arXiv2026

Reflection symmetry in the equal-mass $1+N$ coorbital problem for $5\leq N\leq8$

We study reflection symmetry in the equal-mass Newtonian $1+N$ coorbital problem for $N=5,6,7,8$. We prove that every collision-free solution of the angular central-configuration equations has a reflection axis. As a consequence, every non-coalescent limit of planar central configurations consisting of one dominant mass and $N$ equal small masses is reflection-symmetric about a line through the dominant body. Our proof combines analytic arguments with rigorous computer-assisted verification. For each possible reflection, we introduce variables that measure the deviation from that reflection and vanish exactly when the configuration has that symmetry. The central-configuration equations yield a symmetric matrix equation in these variables. Concavity of the force derivative and estimates of the resulting quadratic forms reduce the symmetry problem to finitely many rigorously verified inequalities. Although the details depend on $N$, the same general method applies in all four cases. We also obtain, as a separate result, the complete three-class classification for $N=5$, up to the natural equivalences.

math.DS↗

arXiv2026

Stability-Preserving Reinforcement Learning for Heterogeneity-Aware Composite Max-Pressure Traffic Signal Control

Reinforcement learning (RL) provides a flexible mechanism for adapting traffic signal control to heterogeneous traffic and sensing conditions, but directly learned signal actions do not automatically inherit the analytical properties of structured traffic-control methods. This paper proposes Com-MP, a theory-guided RL framework that learns a context-dependent composition of multiple max-pressure (MP) control preferences while retaining decentralized MP phase selection. The learned policy adapts the relative influence of constituent MP formulations according to local traffic and sensing conditions, allowing data-driven adaptation to operate within a structured traffic-control framework. We show that such intersection-specific and time-varying composition preserves strong queue stability for every demand in the strictly stabilizable region under any admissible non-anticipative composition policy, thereby separating the performance-adaptation role of learning from the stability property of the underlying controller. In a representative implementation combining detector-supported queue-based MP and connected-vehicle-supported travel-time MP, experiments on a real-world 45-intersection network show that Com-MP reduces average delay by 15.6\% and 8.6\% relative to the two constituent controllers, respectively, and by about 7.0\% relative to the best fixed composition. The learned composition responds systematically to local traffic and sensing conditions, remains effective under heterogeneous and degraded sensing, and can be transferred without retraining to an unseen network with an average delay only 2.4\% higher than that of a policy trained directly on the target network. These results show how learning-based adaptation can be introduced within a stability-preserving traffic-control structure, providing a theory-guided pathway toward trustworthy learning-enabled traffic signal control.

eess.SY↗

arXiv2026

Multichoice Modeling: Exploring Decision Configuration Space under Uncertainty

Decision support has become sophisticated at exploring uncertainty, but much less so at representing the architecture of the decision itself. As a result, the decision space is often narrowed before uncertainty is analyzed, leaving interactions among choices and the effects of alternatives they imply largely invisible. This paper introduces multichoice modeling, a framework for making large decision configuration spaces explicit and computationally explorable under uncertainty. Drawing on the logic of rugged landscapes, we conceptualize such problems as contingent performance landscapes, where interdependent choices generate configuration-specific outcomes whose value changes across uncertain futures. The computational framework combines multidimensional decision and uncertainty spaces in a single simulation. Further, variance-based sensitivity analysis is used for identifying influential choices, and conditional distribution analysis for comparing configuration-specific performance profiles. We demonstrate the framework through three case studies: a manufacturing process upgrade, M&A strategy, and mortgage design. By contrasting conventional uncertainty-only analysis with multichoice modeling, the cases show how opening the decision configuration space can reveal unexpected complementarities, near-best configurations with different risk profiles, and strategies that were not apparent as alternatives at the outset.

cs.AI↗

arXiv2026

ResGVC: Residual Coding for High-fidelity Generative Video Compression

Generative video compression (GVC) methods usually employ decoder-side diffusion models to denoise reconstructed signals based on generative priors. Besides, most of these methods perform denoising in latent space rather than directly in pixel domain. In this paper, we propose ResGVC, a residual coding framework for GVC that guides denoising toward original pictures by transmitting residual signals. ResGVC first encodes the original pictures within a learned video codec, and then decomposes the distortion between the codec reconstruction and the original pictures into a sequence of residual segments, where each residual segment is acquired at each denoising step. Residual segments can further be compressed by a novel residual codec with a diffusion transformer as an entropy model. Unlike prior methods, ResGVC introduces explicit source constraints throughout denoising rather than relying on decoder-side generation alone. The diffusion-based entropy model also enables more effective distribution modeling capability based on the powerful generative priors. Moreover, denoising directly in pixel space avoids the irreversible information loss caused by latent representation bottlenecks. Experimental results show that, compared with the previous state-of-the-art method, ResGVC achieves 63.7% and 83.8% BD-rate reductions in terms of LPIPS and PSNR, respectively, while also delivering superior visual quality.

cs.CV↗

arXiv2026

Set-theoretic inevitability

After defining the concept of inevitability for statements with the modal logic of forcing, we raise the question of which statements are inevitable under $\mathsf{ZFC}$ and under large cardinal hypotheses. We show that $\mathsf{SOA}$ (defined as $\mathsf{ZFC}^-$ + $\mathsf V=\mathsf{HC}$) plus the $\boldsymbolΣ^1_2$-perfect set property is $\mathsf{ZFC}$-inevitable, and that Projective Determinacy is inevitable in the theory of $\mathsf{ZFC}$ with a proper class of Woodin cardinals. We then discuss the possible conceptual significance of these results for the foundations of set theory.

math.LO↗