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Search indexed arXiv papers on artificial intelligence, large language models, computer vision and robotics. Read source abstracts and follow links to arXiv.

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620 records · Page 2Linked to original sources
arXiv2026

A System-of-Systems Case Study for the Verification of Composed Digital Twins

Current approaches to engineering dependable Digital Twins (DTs) of Cyber-Physical Systems lack practical guidance on how qualities such as relevance, verifiability, substitutability and fidelity may be formalised and verified. This need is amplified in Systems-of-Systems (SoS), where reliance is placed on the composition of DTs. The goal of this study is to identify foundational challenges that a framework for DT validation and verification should address in an SoS setting, and to investigate the formalisation of individual DT artefacts as a step towards compositional reasoning. We present a case study based on a DT-enabled greenhouse SoS modelled in VDM-RT (Vienna Development Method, Real-Time), including executable formal models, a property-based account of DT qualities, and an analysis of the obstacles arising when attempting to compose these artefacts at the SoS level. We consider how DT qualities may be operationalised as sets of verifiable properties. Formal modelling and analysis techniques and tools supporting their verification are identified. The study reveals how interpretations of DT qualities must adapt to different architectural roles and how local quality guarantees form assumptions for compositional reasoning. Full formalisation and verification of SoS composition is identified as future work.

cs.SE↗
arXiv2026

Highly Detailed Simulation for Connected Automated Vehicle Cooperative Driving

End-to-end simulation of connected and automated vehicles requires consistent fidelity across mobility, environment modeling, V2X radio propagation, and decision-making/control modules. However, 2D representations of complex road infrastructure often fail to capture critical signal propagation dynamics, leading to overly optimistic connectivity assumptions. This paper presents a unified workflow within CAVISE that integrates map-based scene preparation with microscopic mobility simulation. The proposed framework incorporates a comparative analysis of trace-driven propagation in 3D versus a simplified 2D baseline, and a modular interface for integrating Autonomous Intersection Management (AIM) models. Collectively, these capabilities enable high-fidelity Cooperative Driving Automation (CDA) experiments. Leveraging ray tracing using Sionna RT at 5.9 GHz with the same radio and solver configuration for both geometry variants, we show that planar reduction in multi-level road infrastructure can remove physically present occlusions and substantially distort signal-loss dynamics. In a bridge overpass case study, the 2D baseline eliminates an occlusion interval observed in 3D, changing the outage behavior from intermittent to consistently connected and yielding an average signal-loss shift on the order of 10 dB. These propagation-induced biases highlight the inability of planar models to capture vertical occlusions, necessitating 3D-aware communication modeling to ensure the validity of cooperative driving automation and intersection control evaluations.

cs.NI↗
arXiv2026

Strategic and Grid-Aware Maintenance Planning of Offshore Wind Farms

Wind turbines require regular maintenance and the resulting costs are a substantial component of a wind farm's cost of electricity production. As a result, there has been ongoing interest in improving wind turbine maintenance scheduling to find an optimal balance between maintenance costs and the risk of failure or unplanned repairs. What remains understudied is the opportunity for wind farms to schedule maintenance in the context of grid conditions and electricity market clearing. This paper contributes to closing this gap by modeling and studying wind farm maintenance planning in a grid and electricity market context. We also review current U.S. practice of wind farm maintenance scheduling, which motivates this paper and its models. Our focus is the derivation of a strategic maintenance planning problem, alongside an efficient solution approach, in which the wind farm operator aims to submit a derated wind farm capacity such that the resulting market clearing and electricity prices maximize its profit while ensuring that all required maintenance can be performed. We derive and study both deterministic and stochastic versions of the model, with the latter considering environmental and operational uncertainties. We conduct numerical experiments using the IEEE RTS 96-bus testbed with real-world offshore wind farm data and investigate the roles of farm and turbine size, as well as forecast quality. We observe an alignment between strategic and grid-serving maintenance planning and find that wind farms can improve their bottom line with low impact on system costs.

eess.SY↗
arXiv2026

mmIR: Frequency-Space Inverse Rendering for 3D Millimeter-Wave Radar ADC Synthesis

High-resolution 3D radar data is scarce. Commodity mmWave sensors use small antenna arrays that limit angular resolution to several degrees, and existing datasets provide only 2D range-azimuth maps or sparse point clouds rather than raw analog-to-digital converter (ADC) signals. Hardware scaling is expensive, synthetic-aperture scanning is impractical at fleet scale, and learned synthesis methods are bottlenecked by the very data shortage they aim to address. We present mmIR, an open-source differentiable frequency-modulated continuous-wave (FMCW) radar inverse renderer that fits a physics-based forward model to real captures and re-renders from dense virtual apertures to synthesize high-resolution 3D radar data. Because radar resolution is too coarse to recover geometry directly, mmIR performs LiDAR-assisted inverse rendering: using LiDAR-derived meshes as a geometric scaffold, mmIR optimizes per-vertex International Telecommunication Union (ITU) physics materials, vertex normals, and antenna beam patterns through end-to-end automatic differentiation of a phase-coherent multiple-input multiple-output (MIMO) forward model with multi-bounce propagation, polarization, and free-space diffraction. On seven outdoor and six indoor ColoRadar scenes, mmIR achieves 0.914 mean Pearson correlation on range-azimuth maps versus 0.307 for Sionna-RT. Scenes trained on a cascaded imaging radar transfer to a co-located single-chip radar without re-training (0.554 correlation), and dense virtual arrays (100x100 elements) produce single-frame 3D occupancy validated against LiDAR. Project page: https://mmwave-inverse-rendering.github.io/

cs.CV↗
arXiv2026

REFACTOR-VLA: Unsupervised Library Learning of Typed Motor Programs

Most vision-language-action (VLA) models -- OpenVLA, $π_0$, RT-2, RDT-1B -- are monolithic: they emit raw motor commands or short action chunks without organizing behavior into reusable abstractions, so they degrade on long-horizon tasks and resist interpretation. Existing skill-discovery methods sidestep the core question of when two action sequences are behaviorally equivalent, either clustering contrastive embeddings or delegating the judgment to a language model uncalibrated to the robot's dynamics. We introduce REFACTOR-VLA, a wake/sleep system for learning reusable skills. Its sleep phase clusters motor-program fragments under a Behavioral-Equivalence Kernel (BEK) computed from rollouts of a learned latent world model $M_ϕ$; its wake phase emits typed lambda terms over a Hindley--Milner-inspired vocabulary, consumed by a library-conditioned rectified-flow action decoder. Abstractions are admitted only if they pass Minimum Description Length and return-preservation gates. On LIBERO we report two findings. First, enlarging the world model from 188M to 430M parameters worsened performance on 4 of 4 suites, so capacity alone does not help. Second, the training objective matters far more: adding an auxiliary supervised contrastive (InfoNCE) loss during world-model warmup substantially improves sleep-phase clustering, giving Normalized Mutual Information at $n=3$ seeds of $0.462 \pm 0.021$ (object), $0.867 \pm 0.025$ (spatial), $0.915 \pm 0.013$ (goal) and $0.754 \pm 0.010$ (LIBERO-10), and beating the strongest published baseline on all 4 suites by a mean $Δ= +0.184$. Across providers ($n=12$) the 95% bootstrap confidence interval for mean pairwise NMI is $[0.683, 0.729]$ (mean $0.705$). The sleep phase also yields the first real-LIBERO task-language library: the decoder uses 2 of 3 admitted abstractions and rewrites all 256 sampled demonstrations.

cs.LG↗
arXiv2025

Turing complete Navier-Stokes steady states via cosymplectic geometry

In this article, we construct stationary solutions to the Navier-Stokes equations on certain Riemannian $3$-manifolds that exhibit Turing completeness, in the sense that they are capable of performing universal computation. This universality arises on manifolds admitting nonvanishing harmonic 1-forms, thus showing that computational universality is not obstructed by viscosity, provided the underlying geometry satisfies a mild cohomological condition. The proof makes use of a correspondence between nonvanishing harmonic $1$-forms and cosymplectic geometry, which extends the classical correspondence between Beltrami fields and Reeb flows on contact manifolds.

math.DG↗
arXiv2026

Geometric mean and Lebesgue-type decomposition of completely positive maps

We introduce the geometric mean and the parallel sum of completely positive (CP) maps between von Neumann algebras, based on the Pusz--Woronowicz theory of positive sesquilinear forms. We provide a concrete characterization via a block matrix positivity condition and establish their fundamental properties, including the AM--GM--HM inequality with respect to the CP order. In finite-dimensional settings, our construction is compatible with the Choi--Jamiolkowski correspondence, under which the geometric mean of CP maps corresponds to the Kubo--Ando geometric mean of their Choi matrices. This yields a natural operator-theoretic framework for interpolating quantum channels. As an application, we obtain index-type inequalities for conditional expectations in subfactor theory. Finally, we establish a Lebesgue-type decomposition of CP maps via a parallel sum construction, thereby providing a unified framework that simultaneously generalizes Ando's decomposition of bounded positive operators and Kosaki's decomposition of normal positive functionals on von Neumann algebras.

math.OA↗
arXiv2026

Two Adjoint Perspectives on Fokker-Planck Optimization: A Microscopic-Macroscopic Correspondence

The Fokker-Planck equation admits both a macroscopic Eulerian description through probability densities and a microscopic Lagrangian description through stochastic trajectories. Consequently, optimization problems constrained by the Fokker-Planck equation can be formulated from either perspective. Surprisingly, the corresponding adjoint equations appear to be fundamentally different: the macroscopic adjoint is governed by the backward Kolmogorov equation, whereas the microscopic adjoint evolves pathwise along stochastic trajectories. In this note, we reconcile these two formulations by establishing their correspondence in the continuum setting. We further show that, although their discrete gradients no longer coincide after discretization, both provide consistent numerical approximations of the continuum gradient. Explicit convergence rates are established for both discretization strategies.

math.NA↗
arXiv2026

Multiplicative comparisons of Rényi entropies for weighted Bernoulli sums

We establish improved multiplicative bounds relating the Rényi entropies of different orders for weighted sums of independent Bernoulli random variables. In particular, we prove a logarithmic bound between the zeroth-order and infinity-order Rényi entropies, which yields a polynomial improvement over the square-root bound of Jain, Sah, and Sawhney. Additionally, we obtain explicit constant-factor bounds for comparisons among Rényi entropies of nonzero orders.

math.PR↗
arXiv2026

Harmonic higher weight distributions, Simonis' approach of MacWilliams identity and moments

We present a combinatorial proof of Simonis type MacWilliams identity for harmonic higher weight distributions of linear codes. Furthermore, we investigate the statistical moments of the harmonic higher weight enumerators for random linear codes. Defining the enumerators via rank functions of the generator matrices of linear codes, we prove that its expectation vanishes for all non-trivial harmonic functions due to the inherent symmetry of random matrices, and we also derive an explicit, non-trivial formula for the covariance.

math.CO↗
arXiv2026

Shannon's problem on the monotonicity of entropy and a Conjecture of Tao

Let $X_1,X_2,\ldots$ be i.i.d. finitely supported random variables in a torsion-free abelian group, and write $S_k=X_1+\cdots+X_k$, and $H(S_k)$ is the Shannon entropy $S_k$, for all $k \ge 1$. We prove that, for every fixed $n\geq1$, \[ H(S_{n+1})-H(S_n) \geq \frac12\log\frac{n+1}{n} -o_{H(X_1)\to\infty}(1), \] uniformly over the ambient group and the input law. This proves a conjecture of Tao [29] in 2010.

math.PR↗
arXiv2026

Geometric integrators for adiabatically closed simple thermodynamic systems

A variational formulation for non-equilibrium thermodynamics was developed by Gay-Balmaz and Yoshimura. In a recent article, the first two authors of the present paper introduced partially cosymplectic structures as a geometric framework for thermodynamic systems, recovering the evolution equations obtained variationally. In this paper, we develop a discrete variational principle for adiabatically closed simple thermodynamic systems, which can be utilised to construct numerical integrators for the dynamics of such systems. The effectiveness of our method is illustrated with several examples.

math-ph↗
arXiv2026

Edge codes constructed from unicyclic graphs

Jaramillo-Velez recently introduced edge codes, a new class of toric evaluation codes constructed from the edges of a (hyper)graph $\mathcal{H}$. In the case that $\mathcal{H}$ is a tree, Jaramillo-Velez computed both the minimum distance and the weight distribution of the associated code. In this paper, we study edge codes associated to unicyclic graphs. Our most striking result is that computing the parameters of these codes is subtle in the case that the induced cycle has an even length because these values will depend on certain conditions regarding the length of the cycle and the size of the base field.

math.CO↗
arXiv2026

Difference equations of average entropies

Exact cumulants of entanglement entropies of random state ensembles have traditionally been studied within the random matrix framework. In this work, we propose an alternative approach based on the intrinsic connection to integrable systems. The central idea is to embed entropic quantities into tau functions satisfying Toda-type lattice equations, which in turn yield linear difference equations for their averages. Directly solving the difference equations recovers exact entropy formulas in the literature. The integrable systems approach bypasses the case-by-case, ensemble-dependent derivations required by random matrix methods. The approach also suggests a possible route towards unified and more efficient higher-order cumulant calculations by exploring integrable hierarchies.

math-ph↗
arXiv2026

A Complete Characterization of Tensorizable $f$-divergences

Csiszar's formulation of the $f$-divergence introduced a vast family of functionals for quantifying dissimilarity between probability distributions. However, many applications in statistics and information theory rely only on a few $f$-divergences, such as the Kullback-Leibler divergence, the $χ^2$-divergence, and the squared Hellinger distance. These divergences are especially useful because they admit simple compositional formulas under product measures, a property sometimes referred to as tensorization. In this work, we refine a formalism of tensorization previously introduced in the literature. Then, we show that any possible tensorization formula has a multi-affine form characterized by a single parameter, and identify all tensorizable $f$-divergences under our adopted notion of tensorization.

cs.IT↗
arXiv2026

Spatial symmetry invariance of solution of Kolmogorov flow

We prove a mathematical theorem that solution for all $t > 0$ of the two-dimensional (2D) Kolmogorov flow governed by Navier-Stokes (NS) equations with periodic boundary condition keeps the same spatial symmetry as its smooth initial condition. The proof of a similar theorem for the three-dimensional NS equations is given in the appendix. These mathematical theorems can be used to check the correctness and reliability of numerical simulations of NS turbulence. For example, they support the corresponding CNS (clean numerical simulation) results of the 2D and 3D turbulent Kolmogorov flows [1-3] that remain the same spatial symmetry in the whole time interval of simulation, but do not support the corresponding DNS (direct numerical simulation) results that lose the spatial symmetry quickly. In other words, these DNS results violate these mathematical theorems. Thus, these mathematical theorems rigorously confirm that the spatiotemporal trajectories of NS turbulence given by DNS are indeed quickly polluted by numerical noises badly. All of these indicate that CNS can indeed provide helpful enlightenments to deepen our understanding about turbulence and besides approach some mathematical truths about NS equations.

physics.flu-dyn↗
arXiv2026

A simple derivation of the Kalman filter

In this lecture note, we present a concise and self-contained derivation of the discrete-time Kalman filter equations that requires only a basic understanding of least squares estimation. The treatment is designed to minimize mathematical overhead while preserving both rigor and generality.

math.OC↗