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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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At least 19 recordsLinked to original sources

arXiv2026

Thermodynamics: Extending and Reconstructing of Classical Theoretical Framework

One deep problem that the traditional thermodynamics has faced since the beginning, I call it the predicament of equilibrium state. In this predicament, both the initial and the final states of a given system must be in equilibrium states, and the evolutionary processes from an initial to an final states must be assumed to be a series of quasi-static processes, because in non-equilibrium state, there are two intensive variables that anchored to the system or the locals are ill-defined, the real problem is, we did not know which extensive quantity that the temperature T and the pressure p are anchored to. In the traditional thermo-dynamics: there has neither a state quantity of heat, nor dynamics. This deep problem is derived from the absence of a fundamental physical quantity, the total energy of thermal motion in multiple levels, empirically be called as the heat energy, as a state quantity, which never been defined on its own but only implied within the thermodynamic equations. When the concept of the heat energy has been defined, the anchor that the temperature T and the pressure p are anchored to has been confirmed: the temperature T and the pressure p are the two intensive variables of the heat energy, thus, the predicament of equilibrium state has been completely broken through. What we are seeing is a groundbreaking overall progress, almost all the long-standing tricky problems in the traditional thermodynamics will be finally clarified. In this article, I will discuss some of the famous problems focusing on reconstructing a new theoretical framework: Thermodynamic processes are driven by the gradients of thermodynamic forces, the relationship between the states and the changes of a given system and the driving forces are the main themes of thermodynamics. What we see is a new narrative paradigm: there have both the state quantity of the heat energy, and also dynamics.

physics.chem-ph↗

arXiv2026

Classification of critically fixed anti-Thurston maps

We provide a complete combinatorial classification of critically fixed anti-Thurston maps, i.e., orientation-reversing branched covers of the 2-sphere that fix every critical point. The first step in the proof, and an interesting result in its own right, is a combinatorial classification of critically fixed anti-rational maps as "Schottky maps" associated with certain plane graphs. Both of these classification results heavily rely on an orientation-reversing version of Thurston's theory, including the canonical decomposition of anti-Thurston maps, which we develop in this paper. We use our combinatorial framework to answer special instances of the global curve attractor and twisting problems, and to resolve the Hurwitz existence problem in the setting of critically fixed anti-rational maps. Finally, we give some applications to the study of anti-rational maps with symmetries and to critically fixed anti-polynomials.

math.DS↗

arXiv2026

Introduction to the ADM formalism

The authors present concepts and mathematical developments which give rise to the Hamiltonian formulation of Einstein's general relativity, first introduced by Arnowitt, Deser, and Misner. All the geometrical quantities needed for the construction are explicitly obtained, and examples of some of the application of the formalism are given.

gr-qc↗

arXiv2026

Monotone comparative statics under dual submodularity, with an application to aggregate deferred acceptance

We develop monotone comparative statics for constrained quantity choices generated by convex costs satisfying dual submodularity, meaning that their Legendre-Fenchel conjugates are submodular. We introduce the Q-order, an exchange order for possibly set-valued quantity choices, and prove a dual counterpart of Topkis's theorem. A closed proper convex function is exchangeable in the Q-order if and only if its conjugate is submodular. Exchangeability implies Q-monotonicity of rejected quantities under price and capacity changes; when the conjugate has a sublattice domain, the comparative-statics property is also a characterization. We apply the result to two-sided matching with divisible masses and welfare-generated, possibly set-valued choices. An aggregate deferred-acceptance algorithm is well defined; the availability sequence and the least waiting-time multiplier sequences converge; and every proposal limit selected by the theorem yields an aggregate equilibrium matching. The construction covers classical stable nontransferable-utility matching and aggregate random-utility specifications.

econ.TH↗

arXiv2026

Chain-of-Thought in Neural Code Generation: From and For Lightweight Language Models

Large Language Models (LLMs) have demonstrated remarkable potential in code generation. The integration of Chain of Thought (CoT) reasoning can further boost their performance. However, current CoT methods often require manual writing or LLMs with over 100 billion parameters to generate, impeding their applicability in resource-constrained scenarios. In this study, we investigate lightweight Language Models (lLMs), which are defined to have fewer than 10 billion parameters. Empirically, we find that most lLMs cannot generate high-quality CoTs when prompted by the few-shot method, but can take advantage of high-quality CoTs generated elsewhere to improve their performance in code generation. Based on these findings, we design a novel approach COTTON which can leverage lLMs to automatically generate CoTs for code generation. We synthesize new datasets and conduct extensive experiments on various benchmarks. The results show that the CoTs generated by COTTON outperform the baselines in terms of automated and human evaluation metrics. In particular, the CoTs generated by COTTON boost various lLMs to achieve higher performance gains than those generated by LLMs such as ChatGLM (130B), and are competitive with those generated by gpt-3.5-turbo (175B). Our study also showcases the potential of lLMs in software engineering applications.

cs.SE↗

arXiv2026

Conditional Motional Squeezing of an Optomechanical Oscillator Approaching the Quantum Regime

Squeezed mechanical states are a highly coveted resource for quantum-enhanced sensing and serve as a compelling platform for probing the interplay between gravity and quantum mechanics. It has been predicted that a mechanical oscillator can be prepared into a quantum squeezed state if the applied measurement rate is fast relative to its mechanical resonance frequency. However, the experimental feasibility of this protocol has remained uncertain because of the difficulty in achieving low-frequency oscillators with sufficiently strong read-out. Here, we demonstrate that a careful selection of parameters in an optomechanical system, combined with optimal filtering techniques, enables the preparation of a 50 ng GaAs cantilever in a conditional classical squeezed state, achieving a minimum uncertainty of just 1.07 plus/minus 0.04 times the zero-point fluctuation level. This minimum variance is 3 orders of magnitude smaller than what has been achieved in previous experiments using the same protocol. Although we do not fully achieve the quantum squeezed regime, our demonstration provides definitive evidence that a measurement-based protocol is a practical and effective approach for the real-time preparation of macroscopic oscillators in quantum squeezed states.

quant-ph↗

arXiv2026

Fourier-Mukai partners of abelian varieties and K3 surfaces in positive and mixed characteristics

We study Fourier-Mukai equivalences of (families of) abelian varieties and K3 surfaces in positive and mixed characteristics. We first prove in any characteristics that Fourier-Mukai partners of abelian varieties are again abelian varieties. We subsequently focus on the canonical lifts of ordinary abelian varieties and ordinary K3 surfaces. For such schemes, we show that Fourier-Mukai equivalences on the special fibers can be lifted to the canonical lifts. We also prove that the relative Fourier-Mukai partners of the canonical lifts are in bijection with the Fourier-Mukai partners of the special fibers. We conclude by demonstrating that the last result can be used to recover the ordinary case of a result originally proved by Honigs, Lombardi and Tirabassi.

math.AG↗

arXiv2026

On the complexity of epimorphism testing with virtually abelian targets

Friedl and Löh (2021, Confl. Math.) prove that testing whether or not there is an epimorphism from a finitely presented group to the direct product of an abelian and a finite group, or to a virtually cyclic group, is decidable. Here we prove that these problems are $\mathsf{NP}$-complete. In addition, we show that testing epimorphism is $\mathsf{NP}$-complete when the target is is the semi-direct product of a finitely generated free-abelian group and a finite group which factors through $\{\pm\text{Id}\}$, thus extending the class of virtually abelian target groups for which decidability of epimorphism is known.

math.GR↗

arXiv2026

Partial Markov Categories

We introduce partial Markov categories as a synthetic framework for synthetic probabilistic inference, blending the work of Cho and Jacobs, Fritz, and Golubtsov on Markov categories with the work of Cockett and Lack on cartesian restriction categories. We describe observations, Bayes' theorem, normalisation, and both Pearl's and Jeffrey's updates in purely categorical terms.

math.CT↗

arXiv2026

The $q$-deformed random-to-random family in the Hecke algebra

We generalize Reiner--Saliola--Welker's well-known but mysterious family of *$k$-random-to-random shuffles* from Markov chains on symmetric groups to Markov chains on Type-$A$ Iwahori--Hecke algebras. We prove that these operators pairwise commute, and that their eigenvalues are polynomials in $q$ with non-negative integer coefficients; we express these eigenvalues in a closed form as certain symmetric function evaluations (which is new even for $q=1$). We show that these operators are simultaneously diagonalizable for almost all $q$, and combinatorially express the dimension of the subalgebra they generate. Our work generalizes and extends work of Reiner--Saliola--Welker and Lafrenière for the symmetric group, and simplifies all known proofs in this case.

math.CO↗

arXiv2026

On the Spherical Dirichlet Distribution: Corrections and Results

This article revisits the spherical-Dirichlet distribution (SDD) introduced by Guardiola (2020) and clarifies the correction to its density presented in an earlier version of this preprint. The principal issue concerns Equation (3) of the original publication, which expresses the density in local Euclidean coordinates rather than with respect to spherical surface-area measure. We derive the corrected intrinsic density and revisit its moments, covariance matrix, mode, and limiting properties. We show that the two density representations describe the same probability distribution, preserving the moment formulas and likelihood-based parameter estimation. However, the mode and uniformity conditions depend on the reference measure and require corresponding clarification. Reported simulation and text mining estimates are revisited and updated. The resulting presentation reconciles the original construction with its intrinsic spherical properties.

stat.ME↗

arXiv2026

A Path Planning Model for Intercepting a Moving Target with Finite Obstacle Avoidance

This paper investigates the problem of computing a two-dimensional curvature-constrained shortest path for an unmanned aerial vehicle (UAV) to intercept a moving target, with both the UAV (pursuer) and the target traveling at constant speeds. We formulate an optimal control problem that integrates two critical objectives: avoiding static obstacles and successfully intercepting the target. The formulation integrates curvature constraints, geometric obstacle-avoidance conditions, and time-consistent interception constraints within a constrained optimal control framework. A geometric framework is developed, along with necessary conditions for path optimality under the imposed constraints. The problem is initially examined in the presence of a single obstacle and later extended to scenarios involving a finite number of obstacles. Numerical experiments are carried out to evaluate the performance and efficiency of the proposed model using illustrative examples. Finally, we present a realistic case study using actual geographic data, including obstacle placement, target trajectory, and heading angles, to demonstrate the practical applicability and effectiveness of the proposed method in real-world scenarios.

math.OC↗

arXiv2026

The Atacama Cosmology Telescope: Release of A databaSe of millimeTeR ObservatioNs of Asteroids Using acT ($\mathtt{ASTRONAUT}$)

We present A databaSe of millimeTeR ObservatioNs of Asteroids Using acT ($\mathtt{ASTRONAUT}$) hosted on Amazon Web Services, Inc. (AWS) in the form of a public Amazon Simple Storage Service (S3) bucket. This bucket is an Amazon cloud storage database containing flux measurements for a group of asteroids at millimeter (mm) wavelengths. These measurements were collected by the Atacama Cosmology Telescope (ACT) from 2017 to 2021 in frequency bands centered near 90, 150, and 220 GHz. The $\mathtt{ASTRONAUT}$ database contains observation times, normalized flux values, and associated error bars for 170 asteroids above a signal-to-noise ratio of 5 for a single frequency band over the stacked co-added maps. We provide an example in generating light curves with this database. We also present a Jupyter notebook to serve as a reference guide when using the S3 bucket. The container and notebook are publicly available in a GitHub repository.

astro-ph.EP↗

arXiv2026

Disentangling Latent Embeddings with Sparse Linear Concept Cones (SLiCC)

Pretrained vision models encode semantic information in latent embedding spaces that are useful for downstream tasks. We hypothesize that this information can be disentangled to separate the content of complex scenes by decomposing each embedding into multiple concept-specific components. We propose Sparse Linear Concept Cones (SLiCC), a supervised dictionary learning approach that estimates a linear synthesis model consisting of sparse, non-negative combinations of groups of dictionary atoms, whose group-wise activity is guided by multi-label information. Each concept-specific component is a non-negative combination of atoms associated with a label and lies in a corresponding concept cone. We introduce an alternating optimization algorithm and an autoencoder formulation of SLiCC. We apply SLiCC to three types of CLIP and DINOv2 embeddings across five datasets. For CLIP, we additionally exploit image-text alignment to enable a self-supervised SLiCC. We also introduce a fully unsupervised autoencoder that enforces group sparsity based on the norm of neuron activations. Quantitative results show that supervised SLiCC improves concept-filtered image retrieval over unfiltered embeddings, including retrieval of finer-grained information not provided during training. Beyond retrieval of individual concepts, the disentangled components enable concept deletion and recombination across images. We further explore conditional image generation using Image-to-Prompt, with qualitative results illustrating retrieval and generation from manipulated concept representations.

cs.CV↗

arXiv2026

Lagrangian Stability Analysis Technique for Fluid Flows

Flow transition from a stable to unstable states and eventually to turbulence is a classical fluid mechanics phenomenon with a strong practical relevance. Conventional hydrodynamic stability deals with perturbation dynamics on a steady baseflow, typically in Eulerian reference frame. Common modal techniques, e.g., linear stability theory, involve linearization of governing flow equations and flow/geometrical simplifications, which can be tedious and restrictive. This paper presents a perturbation-free data-driven stability analysis technique by employing Lagrangian modal/non-modal analysis (Shinde & Gaitonde 2021), particularly the adjoint form of Lagrangian dynamics mode decomposition in the forward time direction. The proposed Lagrangian stability analysis technique (LagSAT) builds on the fact that a steady non-uniform fluid flow in the Eulerian reference frame can be perceived as an unsteady flow in the Lagrangian reference frame. LagSAT is demonstrated on classical baseflows that exhibit convective/absolute instabilities, namely, the self-similar Blasius/Falkner-Skan boundary layers, a 2D compressible flow past a cylinder, and a 2D compressible lid-driven cavity flow, producing neutral stability curves, N-factor estimate, and transient energy growth. LagSAT is naturally suitable for the global analysis of large/complex numerical/experimental baseflows with multiphysics effects.

physics.flu-dyn↗

arXiv2026

An upper bound for the list-distinguishing chromatic number of $K_{r,r+1}$-free graphs

In 2006, Collins and Trenk obtained a general sharp upper bound for the distinguishing chromatic number of a connected graph. Inspired by Catlin's combinatorial techniques from 1978, we establish improved upper bounds for classes of connected graphs that have only small complete bigraphs as induced subgraphs. In this framework, we also consider the list-distinguishing chromatic number of such graphs. We apply Menger's theorem to demonstrate applications of our main result for graphs whose constructions are based on Paley graphs and Cayley graphs on Dihedral groups.

math.CO↗

arXiv2026

From Legacy Fortran to Portable Kokkos: An Autonomous Agentic AI Workflow

Scientific applications still rely heavily on legacy Fortran codebases built for homogeneous, CPU-based systems. As High-Performance Computing (HPC) shifts toward GPU-accelerated architectures, many accelerators lack native Fortran bindings, creating a need to translate and optimize legacy code for portability. Kokkos offers performance portability through a single-source C++ abstraction, but manual porting from Fortran demands significant expertise and time. While large language models (LLMs) show promise in source-to-source code generation, their use in autonomous workflows for translating and optimizing parallel code is largely unexplored. This paper presents an agentic AI workflow in which specialized LLM agents collaborate to translate, validate, compile, run, test, debug, and optimize Fortran kernels into portable Kokkos C++ programs without human intervention, bounded by configurable retry and optimization thresholds. We evaluate the pipeline over five runs per configuration on an NVIDIA A100, characterizing its variability in success rates, token cost, and optimization behavior, on benchmark kernels including a real-world multi-file kernel from a production climate model. Proprietary models such as GPT-5 and o4-mini-high completed the full workflow most reliably, producing optimized code that exceeded the Fortran baselines for only a few U.S. dollars, whereas open-weights models such as gpt-oss-120b and Qwen3.5-397B-A17B handled simpler kernels but struggled with complex Kokkos abstractions such as parallel reductions and hierarchical parallelism. This work demonstrates, at the kernel level, the feasibility of agentic AI for Fortran-to-Kokkos transformation and, more broadly, for structured software-engineering tasks such as automated code modernization and refactoring.

cs.SE↗

arXiv2026

Best-of-Majority: Minimax-Optimal Strategy for Pass@$k$ Inference Scaling

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@$k$: the agent may submit up to $k$ responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@$k$ inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with $k$ and the sampling budget $N$. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the $N$ samples before selecting the top-$k$ rewards. We prove that when the sampling budget is $N=\tildeΩ(C^*)$, the regret of BoM is $O(ε_{\mathrm{opt}}+\sqrt{ε_{\mathrm{RM}}^2C^*/k})$, where $C^*$ is the coverage coefficient, $ε_{\mathrm{RM}}$ is the estimation error of the reward model, and $ε_{\mathrm{opt}}$ is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing $N$. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

cs.LG↗