arXiv preprints from January 1, 2026 through September 16, 2026 — 10:52:18 EST
The aim of this article is to present in a self-contained way identities arising in elementary number theory, among which the following one: $$ \sum_{d\mid n}\frac{μ^2(d)}{\varphi(d)\,d^s}=\prod_{p\mid n}\left(1+\frac{1}{(p-1)p^s}\right). $$ This formula expresses a non-trivial divisor sum involving the Möbius function $μ$ and Euler's...
Mechanical metamaterials can be designed to exhibit unique mechanical properties, including tunable auxetic behavior as well as multi-stability, which arise from the geometry and configuration of the constituent building blocks. Lattice-based metamaterials, in particular, provide lightweight platforms where local instabilities can...
Adversarial attacks are widely used to identify model vulnerabilities; however, their validity as proxies for robustness to random perturbations remains debated. We ask whether an adversarial example provides a representative estimate of misprediction risk under stochastic perturbations of the same magnitude, or instead reflects an...
Evaluating Text-to-SQL agents in private business intelligence (BI) settings is challenging due to the scarcity of realistic, domain-specific data. While synthetic evaluation data offers a scalable solution, existing generation methods fail to capture business realism--whether questions reflect realistic business logic and workflows....
Partial differential equations (PDEs) are central to scientific modeling. Modern workflows increasingly rely on learning-based components to support model reuse, inference, and integration across large computational processes. Despite the emergence of various physics-aware data-driven approaches, the field still lacks a unified...
Recent studies demonstrate the effectiveness of Self Supervised Learning (SSL) speech representations for Speech Inversion (SI). However, applying SI in real-world scenarios remains challenging due to the pervasive presence of background noise. We propose a unified framework that integrates Speech Enhancement (SE) and SI models...
This paper presents closed-form evaluations of two new Apéry-like series of weight $4$ that involve harmonic numbers of the form $H_{2k}$. Several key results are derived and subsequently used to establish connections to the main series.
Laplace learning is a semi-supervised method, a solution for finding missing labels from a partially labeled dataset utilizing the geometry given by the unlabeled data points. The method minimizes a Dirichlet energy defined on a (discrete) graph constructed from the full dataset. In finite dimensions the asymptotics in the large...
Reliable early detection of Alzheimer's disease (AD) is challenging, particularly due to the limited availability of labeled data. While large language models (LLMs) have shown strong transfer capabilities across do mains, adapting them to the AD domain through supervised fine-tuning remains largely unexplored. In this work, we...
Probabilistic mental simulation is thought to play a key role in human reasoning, planning, and prediction, yet the demands of simulation in complex environments exceed realistic human capacity limits. A theory with growing evidence is that people simulate using simplified representations of the environment that abstract away from...
We formulate a deterministic algorithm for preparing a general $U(1)$-eigenstate of a spin-$s$ chain of length $n$. These states consist of linear combinations of computational basis states $|\vec{m}\rangle$ of $n$ qudits, each with $(2s+1)$ levels and $s= 1/2, 1, 3/2, \ldots$, whose ditstrings $\vec{m}$ have a fixed digit sum....
The Aiming for AI Interoperability report investigates the ongoing challenge of achieving regulatory and technical AI interoperability as national and global AI governance efforts are proliferating. Here, technical interoperability is the ability of AI systems and networks to function together, and regulatory interoperability is the...
As malware continues to become increasingly sophisticated, threatening, and evasive, malware detection systems must keep pace and become equally intelligent, powerful, and transparent. In this paper, we propose Assembly Flow Graph (AFG) to comprehensively represent the assembly flow of a binary executable as graph data. Importantly,...
Gaussian Splatting (GS) has recently emerged as a state-of-the-art representation for radiance fields, combining real-time rendering with high visual fidelity. However, GS models require storing millions of parameters, leading to large file sizes that impair their use in practical multimedia systems. To address this limitation, this...
Developing epithelial tissues coordinate cell proliferation and mechanical forces to achieve proper size and shape. As epithelial cells tightly adhere together to form the confluent tissue, the distribution of cell areas significantly influences possible patterns of cellular packing and thereby also the mechanics of the epithelium....
Super-time-stepping (STS) methods provide an attractive approach for enabling explicit time integration of parabolic operators, particularly in large-scale, higher-dimensional kinetic simulations where fully implicit schemes are impractical. In this work, we present an explicit STS framework tailored for diffusion operators in...
Dipole mixed modes observed in the oscillation pattern of red giant stars probe the radiative regions in the stellar core. Oscillation spectra of helium-core-burning stars sometimes show extra peaks that remain unexplained by the dipole mixed-mode pattern expected from the coupling of a radiative cavity in the stellar core and a...
Large language models are increasingly deployed in STEM education for personalized instruction and feedback across institutions in high- and low-income countries. These systems are designed to adapt content to student needs, but whether they adapt based on demonstrated ability or demographic signals remains untested at scale. Here we...
In the network security domain, due to practical issues -- including imbalanced data and heterogeneous legitimate network traffic -- adversarial attacks in machine learning-based NIDSs have been viewed as attack packets misclassified as benign. Due to this prevailing belief, the possibility of (maliciously) perturbed benign packets...
In this paper, we extend the results of \cite{BCGS} on refined conjectures by Kurihara and Kolyvagin, allowing primes of any reduction type in the case of Kurihara's conjectures, and inert primes in the underlying imaginary quadratic field in the case of Kolyvagin's. The key innovation is a new approach to the computation of the...
Recent European efforts around digital identity -- the EUDI regulation and its OpenID architecture -- aim high to provide an EU-wide authentication framework. However, its current technical and legislative architecture are based on a limited conceptualization of identity. None of the legal and technical texts involved explicitly...
Non-discrete semigroup $T_1$-topologies on the extended bicyclic semigroup $\mathscr{C}_\mathbb{Z}$ are constructed. Also, we present topological conditions, when a semigroup (shift-continuous) $T_1$-topology on $\mathscr{C}_\mathbb{Z}$ is discrete.
Quadratic unconstrained binary optimization (QUBO) is a field of operations research that is attracting growing interest due to the recent availability of quantum hardware targeted at solving QUBO problems. However, practical adoption is hindered by mathematical intricacy, hardware constraints, and a lack of sound software engineering...
A central unresolved question in the theory of superconductivity is why only a small subset of metallic elements exhibit a superconducting state, whereas many others remain strictly normal. Neither the conventional Bardeen Cooper Schrieffer (BCS) framework nor its extensions involving charge density wave (CDW) or pair density wave...
Theoretical models predict that the Galaxy hosts $10^8$-$10^9$ black holes formed from the complete gravitational collapse of heavy stars and that most of these black holes are isolated, without any companion. Within 15 pc of the Solar System ($\sim 50$ ly), there may be a few black holes. If located inside one of the Local...