arXiv preprints from January 1, 2026 through September 22, 2026 — 04:44:13 EST
Let Y be a random variable satisfying specific moment conditions. This paper introduces and investigates probabilistic heterogeneous Stirling numbers of the second kind and probabilistic heterogeneous Bell polynomials. These structures unify several classical and probabilistic families, including those of Stirling, Lah, Bell and...
Interfering deep ultraviolet (DUV) lasers can induce substantial density modulations in an ozone-doped gas flow via photochemical reactions, creating volume diffraction gratings. These transient optics are immune to target debris and shrapnel and feature orders-of-magnitude higher damage thresholds than conventional solid optics,...
We study stochastic transport of interacting particles on a disordered network described by the random comb geometry. The model is defined on a one-dimensional backbone from which branches of random lengths emanate, providing a minimal model of percolation networks beyond the critical percolation probability. The dynamics obeys local...
The democratization of artificial intelligence through decentralized networks represents a paradigm shift in computational provisioning, yet the long-term viability of these ecosystems is critically endangered by the extreme volatility of their native economic layers. Current tokenomic models, which predominantly rely on static or...
This paper investigates the problem of Leaky Private Information Retrieval with Side Information (L-PIR-SI), providing a fundamental characterization of the trade-off among leaky privacy, side information, and download cost. We propose a unified probabilistic framework to design L-PIR-SI schemes under $\varepsilon$-differential...
Penning trap mass measurements of $^{149}$La, $^{149}$Ce, and $^{149}$Pr were performed with the Canadian Penning Trap (CPT) at the CARIBU facility of Argonne National Laboratory using the phase-imaging ion-cyclotron-resonance technique. The resulting mass excess of $^{149}$La differs by 221 keV from a recent JYFLTRAP measurement,...
Let $G$ be an infinite, connected, locally finite planar graph and consider i.i.d.\ Bernoulli$(p)$ site percolation. Write $p_c^{\mathrm{site}}(G)$ and $p_u^{\mathrm{site}}(G)$ for the critical and uniqueness thresholds. Using a well--separated Freudenthal embedding $G\hookrightarrow\mathbb S^2$, we introduce a cycle--separation...
We design new minimal-subpacketization schemes for information-theoretic private information retrieval on graph-based replicated databases. In graph-based replication, the system consists of $K$ files replicated across $N$ servers according to a graph with $N$ vertices and $K$ edges. The client wants to retrieve one desired file,...
Let $C$ be a smooth projective curve over an algebraically closed field ${\mathbb{F}}$ equipped with the action of a finite group $G$. When $p =\textrm{char}(\mathbb{F})$ divides the order of $G$, the long-standing problem of computing the induced representation of $G$ on the space $H^0(C,Ω^{\otimes m}_C)$ of globally holomorphic...
In this paper, we construct directed strongly regular graphs and divisible design graphs with new parameters merging some basic relations of so-called Tatra associations schemes. We also study the above association schemes, their fusions and isomorphisms.
Vision-language models (VLMs) have advanced rapidly, but their ability to capture spatial relationships remains a blindspot. Current VLMs are typically built with contrastive language-image pretraining (CLIP) style image encoders. The training recipe often flattens images into 1D patch sequences, discarding the 2D structure necessary...
Standardized math assessments require expensive human pilot studies to establish the difficulty of test items. We investigate the predictive value of open-source large language models (LLMs) for evaluating the difficulty of multiple-choice math questions for real-world students. We show that, while LLMs are poor direct judges of...
Reliable traversable area segmentation in unstructured environments is critical for planning and decision-making in autonomous driving. However, existing data-driven approaches often suffer from degraded segmentation performance in out-of-distribution (OOD) scenarios, consequently impairing downstream driving tasks. To address this...
The Variational Quantum Eigensolver (VQE) is a hybrid quantum-classical algorithm for computing ground state energies of molecular systems. We implement VQE to calculate the potential energy surface of the hydrogen molecule (H$_2$) across 100 bond lengths using the PennyLane quantum computing framework on an HPC cluster featuring...
For Bernoulli site percolation on an infinite, connected, locally finite graph $G=(V,E)$, we obtain quantitative upper bounds on the supercritical disconnection probability \[ \mathbb{P}_p(S\nleftrightarrow\infty) \] for arbitrary finite or infinite sets $S\subset V$ and all $p>p^{\mathrm{site}}_c(G)$. The key quantity is a...
Transformers are designed for discrete tokens, yet many real-world signals are continuous processes observed through noisy sampling. Discrete tokenizations (raw values, patches, finite differences) can be brittle in low signal-to-noise regimes, especially when downstream objectives impose asymmetric penalties that rationally encourage...
We present new measurements of galaxy luminosity functions (LFs) from JWST/NIRCam imaging over the redshift range z=4.5-9.7, using photometric catalogs from JADES and public extragalactic fields. Our analysis includes rest-frame UV and B-band LFs, as well as apparent LFs in F090W, F115W, F200W, F356W, and F444W. We present the first...
The sequence reconstruction problem, introduced by Levenshtein in 2001, considers a communication setting in which a sender transmits a codeword and the receiver observes K independent noisy versions of this codeword. In this work, we study the problem of efficient reconstruction when each of the $K$ outputs is corrupted by a $q$-ary...
Metric Differential Privacy (mDP) generalizes Local Differential Privacy (LDP) by adapting privacy guarantees based on pairwise distances, enabling context-aware protection and improved utility. While existing optimization-based methods reduce utility loss effectively in coarse-grained domains, optimizing mDP in fine-grained or...
For the accelerator magnets of the next hadron collider, reducing superconductor persistent-current magnetization is not only important for achieving the desired field quality, but also crucial for its sustainability because the magnetization loss is the major heat load to the magnet cold mass. For conventional Nb3Sn conductors this...
University engineering capstone projects involve sustained interaction among students, faculty, and industry sponsors whose objectives are only partially aligned. While capstones are widely used in engineering education, existing analyses typically treat stakeholder behavior informally or descriptively, leaving incentive conflicts,...
Quantum Computing (QC) has evolved from a few custom quantum computers, which were only accessible to their creators, to an array of commercial quantum computers that can be accessed on the cloud by anyone. Accessing these cloud quantum computers requires a complex chain of tools that facilitate connecting, programming, simulating...
The choice of the tuning parameter in the Lasso is central to its statistical performance in high-dimensional linear regression. In this work, we study tuning regimes under which the Lasso exhibits suboptimal prediction performance, in the sense that a simple refinement improves upon it both on high-probability events and in mean...
Recent works have identified that rapidly rotating stars are predominantly binaries with separations of a few to a few tenths of au. This is a crucial range of separation that is often inaccessible to searches of binary stars, providing a unique opportunity to examine their statistical properties. In particular, we have performed an...
Generalized Category Discovery (GCD) aims to classify instances from both known and novel categories within a large-scale unlabeled dataset, a critical yet challenging task for real-world, open-world applications. However, existing methods often rely on pseudo-labeling, or two-stage clustering, which lack a principled mechanism to...