arXiv subjects

Haoxi Hu

Publications and source records attributed to Haoxi Hu.

5 recordsLinked to original sources

arXiv2026

Matroid correspondence

Motivated by algebraic correspondences and linear operators associated with volume and Lorentzian polynomials, we introduce matroid correspondences and their polymatroid analogues. A matroid correspondence defines a functor between poset categories of matroids whose morphisms are matroid quotients, and various standard functors, including deletion, contraction, free extension, truncation, intersection, union, and pullback, arise in this way. We show that these correspondences preserve representability and algebraicity under natural hypotheses. In the polymatroid setting, we establish compatibility with multisymmetric lifts. Finally, we relate this construction to the supports of linear operators with Lorentzian symbols.

math.CO↗

arXiv2026

Graded families of ideals and convex regions

We study the interplay between graded families of ideals in $\mathbb{K}$-domains and their associated convex regions. These regions, called Newton-Okounkov regions, arise naturally from graded families of ideals associated to a valuation with one-dimensional leaves. Our main focus is to compute asymptotic resurgence number of a pair of graded families of ideals. By combining techniques from Attouch--Wets topology and convex-geometric properties of Newton-Okounkov regions, we characterize the asymptotic resurgence number through containment relations between the pair of corresponding Newton-Okounkov regions.

math.AC↗

arXiv2025

Symbolic powers via extension

This article investigates under which conditions the symbolic powers of the extension of an ideal is the same as the extension of the symbolic powers. Our result generalizes the known scenarios. As an application, we prove formulas for the resurgence of sum of two homogeneous ideals in finitely generated k-algebra domains, where k is algebraically closed. Initially, these were known for ideals in polynomial rings.

math.AC↗

arXiv2025

Resurgence number of matroidal configuration

This article gives a new upper bound for the resurgence number of symbolic powers of matroidal configuration in the following situations: the height of the matroidal configuration is big, or the height is small, and the corresponding simplicial complex of the matroidal configuration is peaked. The Peaked simplicial complex is a generalization of bipartite graph. Furthermore, the article also gives a clean formula to compute the resurgence number and the strict containment of generalized uniform matroidal configuration which includes case of star configuration of hypersurfaces.

math.AC↗

arXiv2025

Taming Stable Diffusion for Computed Tomography Blind Super-Resolution

High-resolution computed tomography (CT) imaging is essential for medical diagnosis but requires increased radiation exposure, creating a critical trade-off between image quality and patient safety. While deep learning methods have shown promise in CT super-resolution, they face challenges with complex degradations and limited medical training data. Meanwhile, large-scale pre-trained diffusion models, particularly Stable Diffusion, have demonstrated remarkable capabilities in synthesizing fine details across various vision tasks. Motivated by this, we propose a novel framework that adapts Stable Diffusion for CT blind super-resolution. We employ a practical degradation model to synthesize realistic low-quality images and leverage a pre-trained vision-language model to generate corresponding descriptions. Subsequently, we perform super-resolution using Stable Diffusion with a specialized controlling strategy, conditioned on both low-resolution inputs and the generated text descriptions. Extensive experiments show that our method outperforms existing approaches, demonstrating its potential for achieving high-quality CT imaging at reduced radiation doses. Our code will be made publicly available.

eess.IV↗