arXiv preprints from January 1, 2026 through September 29, 2026 — 08:39:02 EST
Waves propagating through a gravitational potential exhibit wave-optics effects when their wavelength is not significantly smaller than the lensing scales. We study the propagation of a scalar wave, governed by the Klein-Gordon equation in curved spacetime, to focus on effects on amplitude and phase, while leaving aside the issue of...
In this paper, we prove that for every $k$ and every graph $H$ with $m$ edges and no isolated vertices, the Ramsey number $R(C_k,H)$ is at most $2m+\lfloor \frac{k-1}{2} \rfloor$, provided $m$ is sufficiently large with respect to $k$. This settles a problem of Erdős, Faudree, Rousseau and Schelp.
Differentially Private Stochastic Gradient Descent (DP-SGD) is the dominant paradigm for private training, but its fundamental limitations under worst-case adversarial privacy definitions remain poorly understood. We analyze DP-SGD in the $f$-differential privacy framework, which characterizes privacy via hypothesis-testing trade-off...
AI writing assistants can reduce effort and improve fluency, but they may also weaken writers' sense of authorship. We study this tension with an ownership-aware co-writing editor that offers on-demand, sentence-level suggestions and tests two common design choices: persona-based coaching and style personalization. In an online study...
We prove an analog of the flower theorem for non-degenerate reduced tangent to the identity germs that fix the coordinate hyperspaces in any dimension.
The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type synchronization through networks of Stuart--Landau oscillators, which arise as the universal normal...
This work addresses the challenge of safe and efficient mobile robot navigation in complex dynamic environments with concave moving obstacles. Reactive safe controllers like Control Barrier Functions (CBFs) design obstacle avoidance strategies based only on the current states of the obstacles, risking future collisions. To alleviate...
Understanding complex parameter dependencies is critical for effective configuration and maintenance of software systems across diverse domains - from Computer-Aided Engineering (CAE) to cloud infrastructure and database management. However, legacy tabular interfaces create a major bottleneck: engineers cannot easily comprehend how...
A proof will be presented that the existence of a non-trivial $Σ_1$-elementary embedding $j: V_{λ+3} \prec V_{λ+3}$ is inconsistent with $\textsf{ZF}$. Sections 1 and 2 shall review various important contributions from the literature, notably including \cite{Goldberg2020}, \cite{Schlutzenberg2020}, and \cite{Woodin2010}, the latter...
Despite the significant role of turbomachinery in fluid-based energy transfer, precise simulation of rotating solid objects with complex geometry is a challenging task. In the present study, the volume penalization method (VPM) is combined with multiple reference frame (MRF) and sliding mesh (SLM), respectively, so as to develop...
Recent advances in Large Language Models (LLMs) have demonstrated remarkable progress in their reasoning capabilities, such as Chain-of-Thought (CoT). Most approaches rely on CoT rationales. Previous studies have shown that LLMs often generate logically inconsistent reasoning steps even when their final answers are correct. These...
Multimodal Large Language Models (MLLMs) struggle with complex video QA benchmarks like HD-EPIC VQA due to ambiguous queries/options, poor long-range temporal reasoning, and non-standardized outputs. We propose a framework integrating query/choice pre-processing, domain-specific Qwen2.5-VL fine-tuning, a novel Temporal...
This article investigates structural connections between unrefinable partitions into distinct parts and numerical semigroups. By analysing the hooksets of Young diagrams associated with numerical sets, new criteria for recognising unrefinable partitions are established. A correspondence between missing parts and the gaps of...
The variable range hopping (VRH) model has been widely applied to describe electrical transport in disordered systems, providing theoretical formulas to fit temperature-dependent electric conductivity. These models rely on oversimplified assumptions that restrict their applicability and result in problematic fitting behaviors, yet...
Origami-inspired structures with rigid panels now span thick, kirigami, and multi-sheet realizations, making unified kinematic analysis essential. Yet a general method that consolidates their loop constraints has been lacking. We present an automated approach that generates the Pfaffian constraint matrix for arbitrary rigid foldable...
Innovation emerges from complex collaboration patterns - among inventors, firms, or institutions. However, not much is known about the overall mesoscopic structure around which inventive activity self-organizes. Here, we tackle this problem by employing patent data to analyze both individual (co-inventorship) and organization...
People who stutter (PWS) face systemic exclusion in today's voice-driven society, where access to voice assistants, authentication systems, and remote work tools increasingly depends on fluent speech. Current automatic speech recognition (ASR) systems, trained predominantly on fluent speech, fail to serve millions of PWS worldwide. We...
Optimization is central to both modern machine learning (ML) and scientific machine learning (SciML), yet the structure of the underlying optimization problems differs substantially across these domains. Classical ML typically relies on stochastic, sample-separable objectives that favor first-order and adaptive gradient methods. In...
Learning, inference, memory, and emergence in biological and artificial systems are often described using disparate theoretical frameworks. Here we develop a cognitive field theory in which cognition is described as a collective nonequilibrium phenomenon governed by the geometry and collective spectrum of a learned cognitive manifold....
A new transformation is underway in software engineering, driven by the rapid adoption of generative AI in development workflows. Similar to how version control systems once automated manual coordination, AI tools are now beginning to automate many aspects of programming. For embedded software engineering organizations, however, this...
We present a ground-up redesign of the undergraduate physics degree at Loughborough University, driven by the principle of authenticity in academic and industrial practice. Departing from conventional incremental reforms, we adopt a systems-engineering approach to programme-level curriculum design, treating the degree as an integrated...
This paper reviews the main network analysis methods used to measure structural power, which refers to the ability to shape outcomes through network position and influence, and the ability to affect others through network connections. These approaches have been applied in fields such as corporate control, global value chains, and...
We characterize the nuclearity of Toeplitz operators $T_μ: F_α^p \to F_α^q$ with Borel measure symbols for $1\leq p,q\leq \infty$. For positive measures $μ$ and $q\leq p$, we provide necessary and sufficient conditions in terms of the Berezin transform and establish a rigidity property for nuclearity across this range. In the case...
This work investigates biharmonic and interpolating sesqui-harmonic vector fields on the tangent bundle of a para-Kähler--Norden manifold (M, varphi, g) endowed with the varphi-Sasaki metric. We derive the first variation of the bienergy and interpolating sesqui-energy functionals, restricted to the space of vector fields. Explicit...
In enterprise datasets, documents are rarely pure. They are not just text, nor just numbers; they are a complex amalgam of narrative and structure. Current Retrieval-Augmented Generation (RAG) systems have attempted to address this complexity with a blunt tool: linearization. We convert rich, multidimensional tables into simple...