arXiv preprints from January 1, 2026 through September 13, 2026 — 21:43:54 EST
It is well-known that Leonard pairs have a close connection with bispectral orthogonal polynomials of the Askey scheme. In this paper, we introduce the notion of a Leonard trio $(V,\oV,Z)$, an algebraic structure extending Leonard pairs, for which the overlap coefficients of eigenfunctions of $V$ and $\oV$ are biorthogonal rational...
We show that the bipartite separability of a pure qubit state hinges critically on the combinatorial structure of its computational-basis support. Using Boolean cube geometry, we introduce a taxonomy that distinguishes support-guaranteed separability from cases in which entanglement depends on probability amplitudes. We provide...
The theoretical relationship between the macroscopic textural quality and microscopic structural quality appearing in the phase inversion processes from fresh cream via whipped cream to butter is revealed by the multi-scale simulation of coupled map lattice (CML) based on the mesoscopic elementary processes of the emulsion interfaces....
Current evaluation methods for Retrieval Augmented Generation (RAG) suffer from \textit{factual myopia}: they relentlessly emphasize factual accuracy yet neglect global logical integrity in long-form answer generation. This drives models to force unnatural connections, producing factually grounded yet logically incoherent responses...
Federated Learning (FL) has emerged as a powerful paradigm for decentralized model training, yet it remains vulnerable to deep leakage (DL) attacks that reconstruct private client data from shared model updates. While prior DL methods have demonstrated varying levels of success, they often suffer from instability, limited fidelity, or...
The standardization of the sixth-generation (6G) has recently commenced to address the rapidly growing demands for enhanced wireless network services. Nevertheless, existing wireless systems, particularly at the physical layer waveform level, remain inadequate for achieving the ambitious key performance indicators (KPIs) envisioned...
Large language models (LLMs) have demonstrated strong reasoning, planning, and communication abilities, enabling them to operate as autonomous agents in open environments. While single-agent systems remain limited in adaptability and coordination, recent progress has shifted attention toward multi-agent systems (MAS) composed of...
Partial differential equations (PDEs) form the backbone of simulations of many natural phenomena, for example in climate modeling, material science, and even financial markets. The application of physics-informed neural networks to accelerate the solution of PDEs is promising, but not competitive with numerical solvers yet. Here, we...
The formation and entrapment of gas bubbles during solidification significantly influence the microstructure and mechanical properties of materials, from metallic alloys to ice. While gas segregation at the solidification front is well-documented, the real-time dynamics of bubble nucleation, growth, and engulfment-and their dependence...
We prove the following isoperimetric-type inequality: for every convex body $K$ in $\mathbb R^n$ and some $σ\subset[n]:=\{1,\dots,n\}$ there exists a suitable Hanner polytope $B_K$ with the same volume as $K$ and such that the volume of each of its orthogonal projections onto every subspace whose basis is formed by the canonical...
In this paper, we prove an extension of the noncompact version of Llarull's theorem due to Zhang and Li-Su-Wang-Zhang, giving an upper bound for the infimum of scalar curvature in terms of the bottom spectrum of the Laplacian. Moreover, we extend the theorem to manifolds with boundary, relaxing the strict positivity condition on the...
Deep learning models for brain tumor analysis require large and diverse datasets that are often siloed across healthcare institutions due to privacy regulations. We present a federated learning framework for brain tumor localization that enables multi-institutional collaboration without sharing sensitive patient data. Our method...
The increasing deployment of deep learning systems requires systematic evaluation of their reliability in real-world scenarios. Traditional gradient-based adversarial attacks introduce small perturbations that rarely correspond to realistic failures and mainly assess robustness rather than functional behavior. Generative test...
This paper presents an innovative offshore solution where oil & gas platform clusters are powered by a wind farm and a hydrogen hub. The results show a feasible off-grid design as an alternative to conventional electrification solutions. To address the challenges of design and operation of such a system, a power system model of the...
Dexterous grasping in cluttered environments presents substantial challenges due to the high degrees of freedom of dexterous hands, occlusion, and potential collisions arising from diverse object geometries and complex layouts. To address these challenges, we propose CADGrasp, a two-stage algorithm for general dexterous grasping using...
The electric vehicle routing problem with time windows (EVRPTW) is a complex optimization problem in sustainable logistics, where routing decisions must minimize total travel distance, fleet size, and battery usage while satisfying strict customer time constraints. Although deep reinforcement learning (DRL) has shown great potential...
Open-domain Relational Triplet Extraction (ORTE) is the foundation for mining structured knowledge without predefined schemas. Despite the impressive in-context learning capabilities of Large Language Models (LLMs), existing methods are hindered by their reliance on static, heuristic-driven prompting strategies. Due to the lack of...
Factorizable joint shift (FJS) represents a type of distribution shift (or dataset shift) that comprises both covariate and label shift. Recently, it has been observed that FJS actually arises from consecutive label and covariate (or vice versa) shifts. Research into FJS so far has been confined mostly to the case of categorical...
The paper investigates quantitative weak mixing of Salem substitutions flows. We prove that for a substitution whose substitution matrix is irreducible over the rationals and the dominant eigenvalue is a Salem number, for almost every suspension flow with a piecewise constant roof function, quantitative weak mixing holds with a rate...
Driver distraction remains a leading contributor to motor vehicle crashes, necessitating rigorous evaluation of new in-vehicle technologies. This study assessed the visual and cognitive demands associated with an advanced Large Language Model (LLM) conversational agent (Gemini Live) during on-road driving, comparing it against...
We obtain the generic real Jordan canonical forms for $n\times n$ matrices with real entries. More precisely, we prove that the set of $n\times n$ real matrices is the union of the closures of $\lfloor n/2\rfloor+1$ sets, which are called generic bundles, as they are particular "bundles". In general, a bundle is the set of $n\times n$...
Functional bilevel optimization (FBO) provides a powerful framework for hierarchical learning in function spaces, yet current methods are limited to static offline settings and perform suboptimally in online, non-stationary scenarios. We propose SmoothFBO, the first algorithm for non-stationary FBO with both theoretical guarantees and...
Cortical gamma ($γ$)-band activity reflects local excitation-inhibition (E/I) balance. In schizophrenia (SCZ), reduced task-evoked gamma suggests altered E/I dynamics, but it is unclear whether differences stem from input properties or systematic shifts in E/I operating point and gain. We coupled a cochlear-inspired speech front end...
Magnons in antiferromagnets exhibit two chiral modes, providing an intrinsic degree of freedom for magnon-based computing architectures and spintronic devices. Electrical control of chiral splitting is crucial for applications, but remains challenging. Here, we propose the concept of extrinsic chiral splitting, involving alternating...
We investigate collapsar models with and without self-gravity under identical initial conditions to directly compare the effects of self-gravity on jet properties, such as opening angle, jet power, terminal Lorentz factor, and its variability. We compute a suite of time-dependent, three-dimensional GRMHD simulations of collapsars in...