arXiv preprints from January 1, 2026 through September 21, 2026 — 09:28:11 EST
For a crystal group $Γ$ in dimension $n$, a closed subspace $\mathcal{V}$ of $L^2(\mathbb{R}^n)$ is called $Γ$--shift invariant if, for every $f\in\mathcal{V}$, the shifts of $f$ by every element of $Γ$ also belong to $\mathcal{V}$. The main purpose of this paper is to provide a characterization of the $Γ$--shift invariant closed...
The Instruction Set Architecture (ISA) defines processor operations and serves as the interface between hardware and software. As an open ISA, RISC-V lowers the barriers to processor design and encourages widespread adoption, but also exposes processors to security risks such as functional bugs. Processor fuzzing is a powerful...
We study privacy amplification by shuffling for binary-input local randomizers with a fixed finite output alphabet and full support. For a dataset containing exactly k ones among n users, let T_{n,k} denote the shuffled histogram law. For fixed-composition neighboring shuffled histogram laws in the interior regime, we identify the...
DarkSide-20k (DS-20k) is a next-generation dual-phase liquid argon (LAr) time projection chamber (TPC) devoted to the direct-detection of dark matter. The detector is currently under construction in Hall-C at the Laboratori Nazionali del Gran Sasso, Italy, at a depth of approximately 3500 m water equivalent. The detector will...
Ensuring safety is a critical challenge in applying Reinforcement Learning (RL) to real-world scenarios. Constrained Reinforcement Learning (CRL) addresses this by maximizing returns under predefined constraints, typically formulated as the expected cumulative cost. However, expectation-based constraints overlook rare but high-impact...
Herbig Ae/Be stars (HAeBes) are critical tracers of intermediate- and high-mass star formation, yet their census remains incomplete compared to low-mass young stellar objects like T-Tauri stars. To expand the known population, we systematically searched for HAeBes in LAMOST DR7 low-resolution spectra. Following Sun et al., we applied...
In this paper we analyze the Finnish road network as a graph in order to measure whether the "rurality" or "urbanity" of an area correlates with local geometrical properties of the graph. Our primary motivation is the observation that the road systems in rural areas look similar to hyperbolic graphs, while in large cities they...
The exploration of vast genotype spaces poses fundamental challenges for evolving populations. As the number of genotypes encoding viable phenotypes grows exponentially with genome length, populations can only explore a tiny fraction of these immense spaces, a fact consistently supported by empirical and theoretical evidence....
CP-PAW is a combined electronic structure and ab-initio molecular dynamics code to perform mixed quantum and classical simulations of atomistic condensed phase systems, such as solids, liquids, and molecular systems. As the name suggests, the CP-PAW code unifies the all-electron projector augmented-wave method with the Car-Parrinello...
Autonomous systems often operate in multi-agent settings and need to make concurrent, strategic decisions, typically in uncertain environments. Verification and control problems for these systems can be tackled with concurrent stochastic games (CSGs), but this model requires transition probabilities to be precisely specified - an...
The rapid integration of AI algorithms in safety-critical applications such as autonomous driving and healthcare is raising significant concerns about the ability to meet stringent safety standards. Traditional tools for formal safety verification struggle with the black-box nature of AI-driven systems and lack the flexibility needed...
We address issues related to the presence of defects at finite-temperature topological transitions, in particular when defects are modeled in terms of further variables associated with a quenched disorder, corresponding to the limit in which the defect dynamics is very slow. As a paradigmatic model, we consider the classical...
In this paper, inspired by the multigrid method, we propose a multi-level deep framework for deep solvers. Overall, it divides the entire training process into different levels of training. At each level of training, an adaptive sampling method proposed in this paper is first employed to obtain new training points, so that these...
We derive a hydrodynamic model for the motion of inertial particles with a spherical hard core, interacting through lubrication forces and pairwise repulsive forces. The repulsion arises from the assumption that each particle is surrounded by a thin rough layer of reduced permeability. We prove that, as the number of particles tends...
Generative AI challenges traditional assessments by allowing students to produce correct answers without demonstrating understanding or reasoning. Rather than prohibiting AI, this work argues that one way to integrate AI into education is by creating uncertain situations with the help of AI models and using thinking-oriented teaching...
Intrusion detection systems (IDS) are essential for protecting computer systems and networks against a wide range of cyber threats that continue to evolve over time. IDS are commonly categorized into two main types, each with its own strengths and limitations, such as difficulty in detecting previously unseen attacks and the tendency...
We present a detailed analysis of the old, extended stellar component of the Local Group dwarf galaxy IC 10 using deep resolved-star photometry in the VIS and NISP bands of the Euclid Early Release Observations. Leveraging Euclid's unique combination of wide field of view and high spatial resolution, we trace red giant branch (RGB)...
NoSQL Injection attacks are a class of cybersecurity attacks where an attacker sends a specifically engineered query to a NoSQL database which then performs an unauthorized operation. To defend against such attacks, rule based systems were initially developed but then were found to be ineffective to innovative injection attacks hence...
Learning robust audio-visual embeddings requires bringing genuinely related audio and visual signals together while filtering out incidental co-occurrences - background noise, unrelated elements, or unannotated events. Most contrastive and triplet-loss methods use sparse annotated labels per clip and treat any co-occurrence as...
We study conjugacy limits of certain of subgroups inside $\SL(2,\R)\ltimes\R^2$. These subgroups have a common feature that any two in the same category are conjugates of each other.
We present a theory of the emission spectrum of magnetoexcitons interacting with a $ν= 1$ quantum Hall state of massive Dirac fermions in monolayer transition metal dichalcogenides in high magnetic fields. Using an ab initio-parametrized massive Dirac fermion model including valley and spin degrees of freedom, combined with exact...
We investigate a class of non-quasi-homogeneous free divisors in the sense of Saito. These divisors are defined by equations of the form $D:= \{h=0\}$ on $\mathbb{C}^p$, where the polynomial $h$ is specific linear combination of monomials involving the product of coordinates. For this class, we explicitly construct a Saito basis for...
We establish Flat Torus Theorem type results for groups acting on small cancellation complexes satisfying C(6), C(4)-T(4) and C(3)-T(6) conditions. For C(3)-T(6) complexes the result closely parallels the CAT(0) setting. For C(6) complexes we prove an analogous theorem using a refined notion of flat, exploiting the relationship...
Automated optimization modeling via Large Language Models (LLMs) has emerged as a promising approach to assist complex human decision-making. While post-training has become a pivotal technique to enhance LLMs' capabilities in this domain, its effectiveness is severely constrained by the scarcity and underutilization of high-quality...
In driver activity monitoring, movements are mostly limited to the upper body, which makes many actions look similar. To tell these actions apart, human often rely on the objects the driver is using, such as holding a phone compared with gripping the steering wheel. However, most existing driver-monitoring datasets lack accurate...