arXiv preprints from January 1, 2026 through September 22, 2026 — 01:57:39 EST
Let $p(n)$ denote the number of partitions of a natural number $n$. As $ n \to \infty$, the $n$th root of $p(n)$ tends to $1$, which is related to the Cauchy--Hadamard test for power series. Andrews also discovered an elementary proof. Sun conjectured that this happens in a certain way for $n\geq 6$: \begin{equation*} \sqrt[n]{p(n)} >...
Let $F$ be a Parseval frame in a Hilbert space and let $E$ be a set of real numbers. From these data, we construct an operator $H_{E,e}$ and a positive operator-valued measure (POVM) $F_{E,e}$. This paper investigates in detail the relationship between the operator $H_{E, e}$ and the POVM $F_{E,e}$. Our results extend the classical...
We study the features of scarred eigenstates of relativistic neutrino billiards (NBs), graphene billiards (GBs) and Haldane graphene billiards (HGBs) and recapitulate those for nonrelativistic quantum billiards (NRQBs) with the shapes of a full- and quarter-stadium billiard. Here, we restrict for the GBs and HGBs to the region of...
Dark matter dominates the matter content of the Universe, and its properties can be constrained through large-scale structure probes such as the cross-correlation between the unresolved gamma-ray background (UGRB) and weak gravitational lensing. We analysed 15 years of Fermi-LAT data, constructing UGRB intensity maps in ten energy...
For linear partial differential equations with known fundamental solutions, this work introduces a novel operator learning framework that relies exclusively on domain boundary data, including solution values and normal derivatives, rather than full-domain sampling. By integrating the previously developed Mathematical Artificial Data...
We show that a vast class of finitary fragments of geometric logic admit a form of Craig interpolation property. In doing so, we provide a new dictionary to import technology from algebraic logic to categorical logic.
Online disinformation poses an escalating threat to society, driven increasingly by the rapid spread of misleading content across both multimedia and multilingual platforms. While automated fact-checking methods have advanced in recent years, their effectiveness remains constrained by the scarcity of datasets that reflect these...
Federated learning (FL) for large language models (LLMs) has attracted increasing attention as a privacy-preserving approach for adapting models over distributed data, where parameter-efficient methods such as Low-Rank Adaptation (LoRA) are widely adopted to reduce communication and memory costs. However, practical deployments often...
Establishing precise traceability between embedded systems datasheets and their corresponding code implementations remains a fundamental challenge in systems engineering, particularly for low-level software where manual mapping between specification documents and large code repositories is infeasible. Existing Traceability Link...
Interacting with video games is challenging for people with upper-limb impairments, especially when multiple hand-based inputs are required in rapid succession. Human cooperation, where another person assists the player, has been proposed as a solution, but it is limited by copilot availability and co-location. An alternative is...
We study model-free policy learning for discrete-time mean-field control (MFC) problems with finite state space and compact action space. In contrast to the extensive literature on value-based methods for MFC, policy-based approaches remain largely unexplored due to the intrinsic dependence of transition kernels and rewards on the...
For an integer $n\geq1$, consider a random partition $Π_{n}$ of $\{1,\ldots,n\}$ into $K_{n}$ partition sets with $K_{r,n}$ partition subsets of size $r=1,\ldots,n$, and assume $Π_{n}$ distributed according to the Ewens-Pitman model with parameters $α\in]0,1[$ and $θ>-α$. Although the large-$n$ asymptotic behaviors of $K_{n}$ and...
We present a multiwavelength analysis of 850 $μ$m-selected SMGs (deblended S$_{\rm 850}\gtrsim$ 1mJy) in the SSA22 field, where our deepest JCMT/SCUBA-2 observations reach a sensitivity of $σ_{850}\sim$ 0.80mJy beam$^{-1}$. Using multiple identification methods, we have identified 248 deblended SMG candidates for 192 SCUBA-2 sources....
We present T$^\star$, a simple TraceRL-based training curriculum for progressive block-size scaling in masked diffusion language models (MDMs). Starting from an AR-initialized small-block MDM, T$^\star$ transitions smoothly to larger blocks, enabling higher-parallelism decoding with minimal performance degradation on math reasoning...
Here, we introduce a stochastic partial differential equation (SPDE) formulation driven by temporally correlated noise to describe light propagation beyond the standard Markov approximation. By representing the squared refractive index fluctuations as a random field with explicit long-range temporal correlations, we demonstrate that...
We report on the experimental study of the spectral properties of quantum systems consisting of two quantum billiards (QBs), one with chaotic, the other one with integrable classical dynamics, that are coupled to each other via an opening in a common wall. They are compared to those of a special case of the Rosenzweig-Porter model...
In this article, we demonstrate that for any positive integer $n$, the knot surgery $4$-manifold $E(n)_K$ has a handle decomposition without $1$- and $3$-handles. Here, $K$ represents either a fibered two-bridge knot $C(2ε_1, 2ε_2,\cdots, 2ε_{2g})$ ($ε_i \in \{ 1, -1\}$) in Conway's notation or a Stallings knot $K_m$ ($m \in \mathbb{Z}$).
The proliferation of powerful Text-to-Video (T2V) models, trained on massive web-scale datasets, raises urgent concerns about copyright and privacy violations. Membership inference attacks (MIAs) provide a principled tool for auditing such risks, yet existing techniques - designed for static data like images or text - fail to capture...
We present a simple, numerically efficient but highly flexible non-parametric method to construct representations of option price surfaces which are both smooth and strictly arbitrage-free across time and strike. The method can be viewed as a smooth generalization of the widely-known linear interpolation scheme, and retains the...
By contrast with S4, the analysis of local tabularity above IPC has provided a difficult challenge. This paper studies a strengthening of local tabularity - uniform local tabularity - where one demands that all formulas be equivalent to formulas of a given implication depth. Algebraically, this amounts to considering Heyting algebras...
Backdoored and privacy-leaking deep neural networks pose a serious threat to the deployment of machine learning systems in security-critical settings. Existing defenses for backdoor detection and membership inference typically require access to clean reference models, extensive retraining, or strong assumptions about the attack...
We present a production-optimized multi-agent system designed to translate natural language queries into executable Python code for structured data analytics. Unlike systems that rely on expensive frontier models, our approach achieves high accuracy and cost efficiency through three key innovations: (1) a semantic caching system with...
We have performed density functional theory (DFT) calculations to characterize the energetics, and the atomic and electronic structure, of stacking faults in GaN, both in the stable hexagonal wurtzite (wz) phase and in the metastable cubic zincblende (zb) phase. In wz GaN, SFs on the (0001) planes can be divided into three different...
In many scenarios, it is natural to model a plant's dynamical behavior using a hybrid dynamical system influenced by exogenous continuous-time inputs. While solution concepts and analytical tools for existence and completeness are well established for autonomous hybrid systems, corresponding results for hybrid dynamical systems...
Precise QED radiative corrections for low- and high-energy electron-positron colliders are essential for accurate simulations of luminosity processes and precision tests of the Standard Model. We review the historical formulation and the recent developments of the BabaYaga@NLO event generator, which implements a QED Parton Shower...