arXiv preprints from January 1, 2026 through September 18, 2026 — 09:06:17 EST
Let $K$ be a number field with ring of integers $\mathcal{O}$ and $α\in\mathcal{O}$. For any prime ideal $\mathfrak{p}$ of $\mathcal{O}$, we obtain its higher $α$-Wieferich property, which implies a nonexistence theorem for higher Wieferich unramified prime ideals. If $β\in\mathcal{O}$ is relatively prime to $α$ and all prime ideal...
We present SoundPlot, an open-source framework for analyzing avian vocalizations through acoustic feature extraction, dimensionality reduction, and neural audio synthesis. The system transforms audio signals into a multi-dimensional acoustic feature space, enabling real-time visualization of temporal dynamics in 3D using web-based...
We propose a novel expressivity framework for Graph Neural Networks (GNNs) grounded in Boolean function theory, enabling a fine-grained analysis of their ability to capture complex subpopulation structures. We introduce the notion of \textit{Subpopulation Boolean Isomorphism} (SBI) as an invariant that strictly subsumes existing...
The main contribution of this paper resides in providing novel algorithmic advances and analytical insights for the sequential hiring problem, a recently introduced dynamic optimization model where a firm adaptively fills a limited number of positions from a pool of applicants with known values and acceptance probabilities. While...
Autonomous driving relies on accurate perception to ensure safe driving. Collaborative perception improves accuracy by mitigating the sensing limitations of individual vehicles, such as limited perception range and occlusion-induced blind spots. However, collaborative perception often suffers from high communication overhead due to...
Process Reward Models (PRMs) have achieved strong results in complex reasoning, but are bottlenecked by costly process-level supervision. A widely used alternative, Monte Carlo Estimation (MCE), defines process rewards as the probability that a policy model reaches the correct final answer from a given reasoning step. However, step...
The pre-trained transformer demonstrates remarkable generalization ability in natural image processing. However, directly transferring it to magnetic resonance images faces two key challenges: the inability to adapt to the specificity of medical anatomical structures and the limitations brought about by the privacy and scarcity of...
A digraph $G$ is weightable if its edges can be weighted with real numbers such that the total weight in each directed cycle equals 1. There are several equivalent conditions: that $G$ admits a 0/1-weighting with the same property, or that $G$ contains no subdivided "double-cycle" as a subdigraph, or that for every triple of vertices,...
Anomaly detection of multi-temporal modal data in Wireless Sensor Network (WSN) can provide an important guarantee for reliable network operation. Existing anomaly detection methods in multi-temporal modal data scenarios have the problems of insufficient extraction of spatio-temporal correlation features, high cost of anomaly sample...
Intent-Based Networking (IBN) allows operators to specify high-level network goals rather than low-level configurations. While recent work demonstrates that large language models can automate configuration tasks, a distinct class of intents requires generating optimization code to compute provably optimal solutions for traffic...
Although solid-state platforms underpin modern electronics, little is known about how intense ultrashort light pulses carrying orbital angular momentum (OAM) interact with solids. This gap persists even though, for more conventional light-matter interactions, the complex underlying electron dynamics can often be confined to a single...
Recent advances in large Vision-Language Models (VLMs) have provided rich semantic understanding that empowers drones to search for open-set objects via natural language instructions. However, prior systems struggle to integrate VLMs into practical aerial systems due to orders-of-magnitude frequency mismatch between VLM inference and...
Razborov's flag algebra forms a powerful framework for deriving asymptotic inequalities between induced subgraph densities, underpinning many advances in extremal graph theory. This survey introduces flag algebra to computer scientists working in logic, programming languages, automated verification, and formal methods. We take a...
Long documents pose many challenges to current intelligent writing systems. These include maintaining consistency across sections, sustaining efficient planning and writing as documents become more complex, and effectively providing and integrating AI assistance to the user. Existing AI co-writing tools offer either inline suggestions...
We analyze the problem of a free 1D Klein-Fock-Gordon-Majorana (KFGM) particle in an interval. By free, we mean that there is no potential within the interval and that its walls are penetrable; hence, the pertinent energy current density does not vanish at the walls. Certainly, quantization in an interval is not trivial because...
Monotonicity of pairs of operators is an extension of monotonicity of operators, which plays an important role in solving non-monotone inclusions. One of challenging problems in this new tool is how to design the associated mappings to obtain the monotone pairs. In this paper, we solve this problem and propose a Generalized Inertial...
Continued fractions with prescribed structures on sequences of their partial quotients have been intensively studied in the literature. As far as an integer sequence, especially a randomly generated one is concerned, an attractive question is whether it contains arbitrarily long arithmetic progressions. In this paper we study the...
We propose KaoLRM to re-target the learned prior of the Large Reconstruction Model (LRM) for parametric 3D face reconstruction from single-view images. Parametric 3D Morphable Models (3DMMs) have been widely used for facial reconstruction due to their compact and interpretable parameterization, yet existing 3DMM regressors often...
REST APIs, based on the REpresentational State Transfer (REST) architecture, are the primary type of Web API. The OpenAPI Specification (OAS) serves as the de facto standard for describing REST APIs and is crucial for multiple software engineering tasks. Automated OAS generation can help developers identify and correct issues in...
We introduce a novel spatial discretization technique for the reliable and efficient simulation of magnetization dynamics governed by the Landau-Lifshitz (LL) equation. The overall discretization error is systematically decomposed into temporal and spatial components. The spatial error analysis is conducted by formulating the LL...
We investigate the Keller--Segel--(Navier--)Stokes system posed in a smooth bounded domain \(Ω\subset \mathbb{R}^N\) with \(N = 2,3\): \begin{equation*} \begin{cases} n_t + u \cdot \nabla n = Δn - \nabla \cdot \big( n S(n)\nabla c \big), \\[2mm] u \cdot \nabla c = Δc - c + n, \\[2mm] u_t + κ(u \cdot \nabla) u = Δu - \nabla P + n...
In this paper, we consider the following logarithmic Schrödinger equation \[ -Δu + V(x)u = u \log u^{2},\quad x\in\mathbb{R}^{N}. \] Assuming that \(V\in C(\mathbb{R}^{N},\mathbb R)\), \(V\) is bounded away from zero, and \(V(x)\to+\infty\) as \(|x|\to\infty\), we develop a new perturbative variational approach to overcome the...
Predicting problem-difficulty in large language models (LLMs) refers to estimating how difficult a task is according to the model itself, typically by training linear probes on its internal representations. In this work, we study the multilingual geometry of problem-difficulty in LLMs by training linear probes using the AMC subset of...
The exploration-exploitation (EE) trade-off is a central challenge in reinforcement learning (RL) for large language models (LLMs). With Group Relative Policy Optimization (GRPO), training tends to be exploitation driven: entropy decreases monotonically, samples convergence, and exploration fades. Most existing fixes are...
One of the central challenges in visual place recognition (VPR) is learning a robust global representation that remains discriminative under large viewpoint changes, illumination variations, and severe domain shifts. While visual foundation models (VFMs) provide strong local features, most existing methods rely on a single model,...