arXiv preprints from January 1, 2026 through September 8, 2026 — 11:31:35 EST
An element of a finite group is non-vanishing if no irreducible complex character vanishes on it. We prove that every non-vanishing element of a finite solvable group belongs to the Fitting subgroup. The proof combines the reduction of Isaacs, Navarro, and Wolf with an argument using finite symplectic spaces and Clifford theory.
Pantograph arises in electric trains, material modelling, and the modelling of quantum dot lasers. Pantograph integrodifferential equations are integrodifferential equations involving proportional delays; and they appear in fields such as electrodynamics, epidemiology, control theory, astrophysics, economics, and engineering. This...
The capacity of Low Earth Orbit (LEO) to sustain space operations is under mounting pressure from megaconstellations, legacy fragmentation debris, and new payload classes. Existing assessments of orbital capacity and debris evolution are largely deterministic, tracking mean populations of intact satellites and fragments with ordinary...
We study travelling front solutions of a family of degenerate Fisher-KPP equations $u_t=(u^n u_x)_x+u(1-u^n)$, where $n$ is a positive integer. At the minimal wave speed $c_{\rm min}=\tfrac{1}{\sqrt{1+n}}$, these equations admit sharp front solutions, corresponding to an explicit heteroclinic orbit in the travelling wave phase-space....
For $n$ odd, we enumerate rank $n$ complex topological vector bundles on $\mathbb CP^{n+2}$ with prescribed complex $K$-theory class. The answer exhibits a 24-fold periodicity and is closely related to the enumeration of corank $2$ stably trivial vector bundles.
We prove that the heat semigroup on the circle has optimal complete modified logarithmic Sobolev constant \(1\). The proof is based on a matrix-valued Wirtinger inequality and yields the stronger Bogoliubov--Kubo--Mori Fisher information contraction with rate \(e^{-2t}\). As a consequence, the complete tensorization and transference...
Classical results establish that the Lyapunov exponents of an ergodic measure for linear cocycles over hyperbolic systems can be approximated by the Lyapunov exponents of periodic orbits, provided the cocycle is Hölder continuous. A recent counterexample by Bochi demonstrates that this approximation property fails in general if the...
Does multi-agent LLM interaction help or hurt? Some work reports gains from debate (Du et al., 2024), critique loops (Chen et al., 2025), and mixture-of-agents synthesis (Wang et al., 2025), while other work finds that interaction adds cost without improving quality under equal budgets (Tran & Kiela, 2026; Xu et al., 2026; Jarrett et...
The boxicity of a graph $G$, denoted by $box(G)$, is the minimum integer $d\geq 0$ such that $G$ is the intersection graph of axis-parallel boxes in $\mathbb{R}^d$. The class of zero divisor graphs introduced by Beck (1988) is a popular class of graphs and has been studied extensively by several researchers. Suppose $Z(R)$ is the...
Modern AI models such as tabular foundation models and gradient-boosted ensembles can outpredict classical methods, but provide little basis for reasoning about their predictions. High-stakes decisions call for models that are both accurate and interpretable as built. Local linear modeling offers a path forward: a smooth regression...
The continual evolution of malware variants necessitates detection systems that can adapt to new threats without retraining from scratch. However, continually updating models on new data often leads to catastrophic forgetting, where previously learned knowledge is overwritten. While continual learning has been increasingly explored...
Older adults recovering after lower-limb fracture or hip replacement may experience complex recovery trajectories. Most of the time, these clinical aspects are studied in isolation, masking their joint impact on recovery. This study used the MAISON-LLF dataset, which contains multimodal sensor and clinical assessment data from 18...
World models can predict video without learning dynamics that they reliably preserve. We test whether a frozen DreamerV3 trained only on pendulum video learns a scalar that its own latent transition treats as approximately conserved. A label-free search recovers the same energy-like invariant across independently trained conservative...
Earth-system analysis reconstructs changing physical processes from observations that differ in source, scale, timing, and modality. Natural hazards make this work consequential because incomplete evidence can change estimates of severity, exposure, and mechanism. We introduce EarthVerse, a benchmark that evaluates scientific agents...
Vision-Language Models (VLMs) achieve strong performance in visual reasoning tasks, but it remains unclear whether they understand visual relations, or simply employ shortcuts such as language cues or priors. To investigate this, we use the Qwen3-VL-4B (Bai et al., 2025), a modern VLM, to decode how visual information is encoded...
Earth System Models (ESMs) rely heavily on High-Performance Computing (HPC) resources to simulate global climate. As these models evolve, their computational demands continue to grow, driven by three factors: (1) finer spatial grid resolutions, (2) the integration of complex biogeochemical processes (e.g., atmospheric chemistry,...
Historical people may appear under different languages, scripts, and transcription traditions, while distinct individuals may share highly similar or even identical names. This makes historical identity reconciliation more than a problem of string matching or transliteration. We introduce MHER, a provenance-controlled benchmark for...
Artificial intelligence (AI) is transforming measurement in economics. AI models convert unstructured data, such as text and images, into structured variables at low cost, making previously prohibitive measurement feasible at scale. This shifts the bottleneck from finding any scalable measure of a phenomenon to choosing among many...
In panels with sample selection (that may occur due to attrition, nonresponse, etc.), the assumption of selection on observables (missing at random, MAR) is commonly imposed despite often being implausible. However, this assumption becomes testable when a refreshment sample is available. We develop a statistical test of MAR based on a...
Green-patent indicators built on Cooperative Patent Classification Y02 tags are widely used in research, policy, and investment, yet their construct validity has not been audited at corpus scale. We assess whether Y02 is systematically biased and whether that bias may reinforce the ESG innovation disconnect. We introduce an...
We develop a unified approach to optimal grading in an all-pay contest in which a designer assigns a fixed vector of heterogeneous prizes to maximize expected total effort. The approach covers two information regimes and identifies a common principle: iron locally misordered incentive returns and assign prizes assortatively across the...
Constitutions as the formal foundation of a country's legal and political system have important economic and political effects. Yet, we still know little about why constitutions set effective constraints on politicians in some societies, while being largely disregarded in others. Here, we ask if national culture matters for...
Social scientists rely on hypothesis testing to support their research conclusions, but the standard tests are designed for testing one hypothesis rather than adjudicating between rival possibilities. We develop a new framework, "classification testing", as an alternative. Instead of selecting one hypothesis to test, a researcher...
In the empirical sciences, significance thresholds often determine whether findings are treated as evidence of an effect. This paper studies how likely findings that just meet conventional significance thresholds are to remain significant in replications of the same sample size. To answer this question, we estimate the expected...
Traditional statistical tests are poorly suited for the sequential evaluation of probabilistic forecast calibration. We address this limitation in macroeconomic forecasting by applying a new sequential testing method based on e-values. The e-value-based methodology enables anytime-valid inference. It allows practitioners to test...