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On elementary abelian 2-hypergroups
Yu Jiang
https://arxiv.org/abs/2506.05291 https://arxiv.org/pdf/2506.05291

On elementary abelian 2-hypergroups
A hypergroup is called an elementary abelian 2-hypergroup if it is a constrained direct product of the closed subsets of two elements. In this paper, the elementary abelian 2-hypergroups are studied. All closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are determined. The numbers of all closed subsets and all strongly normal closed subsets of the elementary abelian 2-hypergroups are given. A criterion for the isomorphic closed subsets of the elementa…

Compressing Hypergraphs using Suffix Sorting
Enno Adler, Stefan B\"ottcher, Rita Hartel
https://arxiv.org/abs/2506.05023 https://

Compressing Hypergraphs using Suffix Sorting
Hypergraphs model complex, non-binary relationships like co-authorships, social group memberships, and recommendations. Like traditional graphs, hypergraphs can grow large, posing challenges for storage, transmission, and query performance. We propose HyperCSA, a novel compression method for hypergraphs that maintains support for standard queries over the succinct representation. HyperCSA achieves compression ratios of 26% to 79% of the original file size on real-world hypergraphs - outperformi…

DACN: Dual-Attention Convolutional Network for Hyperspectral Image Super-Resolution
Usman Muhammad, Jorma Laaksonen
https://arxiv.org/abs/2506.05041 https:…

DACN: Dual-Attention Convolutional Network for Hyperspectral Image Super-Resolution
2D convolutional neural networks (CNNs) have attracted significant attention for hyperspectral image super-resolution tasks. However, a key limitation is their reliance on local neighborhoods, which leads to a lack of global contextual understanding. Moreover, band correlation and data scarcity continue to limit their performance. To mitigate these issues, we introduce DACN, a dual-attention convolutional network for hyperspectral image super-resolution. Specifically, the model first employs au…

Compact spacelike biconservative hypersurfaces in de Sitter space
Aykut Kayhan
https://arxiv.org/abs/2506.04744 https://arxiv.org/pdf…

Compact spacelike biconservative hypersurfaces in de Sitter space
In this paper, we investigate the geometry of compact spacelike biconservative hypersurfaces with constant scalar curvature in de Sitter space $\mathbb{S}_1^{m+1}(c)$, under some geometric constraints. Our results extend the understanding of rigidity properties of such hypersurfaces in pseudo-Riemannian settings.

Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
Anna-Maria Raukh
https://arxiv.org/abs/2506.04094 https://

Cohomology of hypersurfaces of weighted projective space and the intersection form on $H^2$
Given a hypersurface $i \colon X \hookrightarrow \widetilde{P}^n$ in a weighted projective space, we compute the intersection form on the second cohomology $H^2(X, \mathbb{Z})^{\otimes n-1} \to \mathbb{Z}$ for the purpose of identifying Fano manifolds obtained from smoothing singular Fanos. In the process, we describe the integer cohomology groups $H^k(X, \mathbb{Z})$ for $k

Hermeus' Prototyp Quarterhorse Mk 1 fliegt erstmals
Das US-Luftfahrtunternehmen Hermeus will Hyperschallflugzuge bauen. Der Prototyp Quarterhorse Mk 1 hat seinen Erstflug absolviert.
https://www.

This https://arxiv.org/abs/2505.12894 has been replaced.
initial toot: https://mastoxiv.page/@arXiv_csSI_…

HyperDet: Source Detection in Hypergraphs via Interactive Relationship Construction and Feature-rich Attention Fusion
Hypergraphs offer superior modeling capabilities for social networks, particularly in capturing group phenomena that extend beyond pairwise interactions in rumor propagation. Existing approaches in rumor source detection predominantly focus on dyadic interactions, which inadequately address the complexity of more intricate relational structures. In this study, we present a novel approach for Source Detection in Hypergraphs (HyperDet) via Interactive Relationship Construction and Feature-rich At…

Nim on Integer Partitions and Hyperrectangles
Eric Gottlieb, Matja\v{z} Krnc, Peter Mur\v{s}i\v{c}
https://arxiv.org/abs/2506.04991 https://

Nim on Integer Partitions and Hyperrectangles
We describe PNim and RNim, two variants of Nim in which piles of tokens are replaced with integer partitions or hyperrectangles. In PNim, the players choose one of the integer partitions and remove a positive number of rows or a positive number of columns from the Young diagram of that partition. In RNim, players choose one of the hyperrectangles and reduce one of its side lengths. For PNim, we find a tight upper bound for the Sprague-Grundy values of partitions and characterize partitions wi…

On the geometry of synthetic null hypersurfaces
Fabio Cavalletti, Davide Manini, Andrea Mondino
https://arxiv.org/abs/2506.04934 https://

On the geometry of synthetic null hypersurfaces
This paper develops a synthetic framework for the geometric and analytic study of null (lightlike) hypersurfaces in non-smooth spacetimes. Drawing from optimal transport and recent advances in Lorentzian geometry and causality theory, we define a synthetic null hypersurface as a triple $(H, G, \mathfrak{m})$: $H$ is a closed achronal set in a topological causal space, $G$ is a gauge function encoding affine parametrizations along null generators, and $\mathfrak{m}$ is a Radon measure serving as…

Numerical invariants of hyper-K\"ahler manifolds
Olivier Debarre, Chen Jiang
https://arxiv.org/abs/2506.04177 https://arxiv.org/…

Numerical invariants of hyper-Kähler manifolds
We study various constraints on the Beauville quadratic form and the Huybrechts-Riemann-Roch polynomial for hyper-Kähler manifolds, mostly in dimension 6 and in the presence of an isotropic class. In an appendix, Chen Jiang proves that in general, the Huybrechts-Riemann-Roch polynomial can always be written as a linear combination with nonnegative coefficients of certain explicit polynomials with positive coefficients. This implies that the Huybrechts-Riemann-Roch polynomial satisfies a curi…