arXiv preprints from January 1, 2026 through September 28, 2026 — 05:02:41 EST
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...
We report the discovery of two swallowtail image formations at $z=2.91$ and $z=6.70$ behind the galaxy cluster MS 0451.6-0305 in JWST-NIRCam imaging. We find that in both of the above lensed systems, the complex image morphology cannot be reproduced by simple fold/cusp caustics, and detailed lens modeling reveals higher-order...
Multimodal models excel in English, supported by abundant image-text and audio-text data, but performance drops sharply for other languages due to limited multilingual multimodal resources. Existing solutions rely on machine translation, while advances in multilingual text modeling remain underutilized. We introduce M2M, a lightweight...
This paper investigates reachability analysis for max-plus linear systems (MPLS), an important class of dynamical systems that model synchronization and delay phenomena in timed discrete-event systems. We specifically focus on backward reachability analysis, i.e., determining the set of states that can reach a given target set within...
Recent advances in multimodal learning have significantly enhanced the reasoning capabilities of vision-language models (VLMs). However, state-of-the-art approaches rely heavily on large-scale human-annotated datasets, which are costly and time-consuming to acquire. To overcome this limitation, we introduce V-Zero, a general...
Large programming courses struggle to provide timely, detailed feedback on student code. We developed Mark My Works, a local autograding system that combines traditional unit testing with LLM-generated explanations. The system uses role-based prompts to analyze submissions, critique code quality, and generate pedagogical feedback...
Multimodal clinical prediction is widely used to integrate heterogeneous data such as Electronic Health Records (EHR) and biosignals. However, existing methods tend to rely on static modality integration schemes and simple fusion strategies. As a result, they fail to fully exploit modality-specific representations. In this paper, we...
We will calculate the diquark mass together with the quark-diquark potential. We apply an extended HAL QCD potential method to a baryonic system made up from a static quark and a diquark. Numerical calculations are performed by employing 2+1 flavor QCD gaugeconfigurations generated by CP-PACS and JLQCD Collaborations on a $16^{3}...
In this paper, we propose difficulty-guided sampling (DGS) to bridge the target gap between the distillation objective and the downstream task, therefore improving the performance of dataset distillation. Deep neural networks achieve remarkable performance but have time and storage-consuming training processes. Dataset distillation is...