Tootfinder

Upper Bounds on the Chromatic Index of Linear Hypergraphs
Thomas Murff, Xerxes D. Arsiwalla
https://arxiv.org/abs/2510.07494 https://arxiv.org/pdf/2510.074…

Upper Bounds on the Chromatic Index of Linear Hypergraphs
We address the problem of finding upper bounds on the chromatic index $q(V,E)$ of linear (and loopless) hypergraphs. The first bound we find is defined through a color-preserving group on a proper and minimally edge-colored linear hypergraph, whose orbits serve as a finer partition to the hypergraph's coloring, thereby yielding an upper bound on $q(V,E)$. The next set of theorems in this paper relates to combinatorial properties of hypergraph coloring. Our results suggest a plausible approach t…

Helsinki-based DataCrunch, which aims to become Europe's first AI cloud hyperscaler, raised a €55M Series A, bringing its total funding to €76.5M (Tamara Djurickovic/Tech.eu)
https://tech.eu/2025/09/08/datacrunch-raises-eur5…

DataCrunch raises €55M to boost EU AI sovereignty with green cloud infrastructure
Helsinki-based DataCrunch, a provider of high-performance AI infrastructure, has raised €55 million in a Series A round to scale its compute platform and advance its ambition to become Europe’s first AI cloud hyperscaler.The round was led by byFounders, Skaala, Varma pension fund, and Tesi, with participation from J12 Ventures and angel investors. Debt financing came from Nordea and Armada Credit Partners, alongside Danske Bank, Norion Bank, and Local Tapiola. With this raise, DataCru…

Scalable Sample-to-Population Estimation of Hyperbolic Space Models for Hypergraphs
Cornelius Fritz, Yubai Yuan, Michael Schweinberger
https://arxiv.org/abs/2509.07031 https://

Scalable Sample-to-Population Estimation of Hyperbolic Space Models for Hypergraphs
Hypergraphs are useful mathematical representations of overlapping and nested subsets of interacting units, including groups of genes or brain regions, economic cartels, political or military coalitions, and groups of products that are purchased together. Despite the vast range of applications, the statistical analysis of hypergraphs is challenging: There are many hyperedges of small and large sizes, and hyperedges can overlap or be nested. We develop a novel statistical approach to hypergraphs…

🕶️ Meta launches Hyperscape, technology to turn real-world spaces into VR
https://techcrunch.com/2025/09/17/meta-launches-hyperscape-technology-to-turn-real-world-spaces-into-vr/

Meta launches Hyperscape, technology to turn real-world spaces into VR | TechCrunch
Quest device owners will be able to scan a room in a few minutes, then turn it into an immersive and photorealistic world that's like a digital replica of a real-world space.

Hyperspectral data augmentation with transformer-based diffusion models
Mattia Ferrari, Lorenzo Bruzzone
https://arxiv.org/abs/2510.08363 https://arxiv.org…

Hyperspectral data augmentation with transformer-based diffusion models
The introduction of new generation hyperspectral satellite sensors, combined with advancements in deep learning methodologies, has significantly enhanced the ability to discriminate detailed land-cover classes at medium-large scales. However, a significant challenge in deep learning methods is the risk of overfitting when training networks with small labeled datasets. In this work, we propose a data augmentation technique that leverages a guided diffusion model. To effectively train the model w…

On special values of generalized $p$-adic hypergeometric functions of logarithmic type
Yusuke Nemoto
https://arxiv.org/abs/2509.07895 https://arxiv.org/pdf…

On special values of generalized $p$-adic hypergeometric functions of logarithmic type
We introduce a new type of $p$-adic hypergeometric functions, which are generalizations of $p$-adic hypergeometric functions of logarithmic type defined by Asakura, and show that these functions satisfy the congruence relations similar to Asakura's. We also give numerical computations of the special values of these functions at $t=1$ and prove that these values are equal to zero under some conditions.

Extendable codimension two subvarieties in a general hypersurface
G. V. Ravindra, Debaditya Raychaudhury
https://arxiv.org/abs/2510.08108 https://arxiv.org…

Extendable codimension two subvarieties in a general hypersurface
We exhibit a class of extendable codimension $2$ subvarieties in a general hypersurface of dimension at least $4$ in projective space. As a consequence, we prove that a general hypersurface of degree $d$ and dimension at least $4$ does not support globally generated indecomposable ACM bundles of any rank if their first Chern class $e \ll d$.

Extremal constructions for apex partite hypergraphs
Qiyuan Chen, Hong Liu, Ke Ye
https://arxiv.org/abs/2510.07997 https://arxiv.org/pdf/2510.07997

Extremal constructions for apex partite hypergraphs
We establish new lower bounds for the Turán and Zarankiewicz numbers of certain apex partite hypergraphs. Given a $(d-1)$-partite $(d-1)$-uniform hypergraph $\mathcal{H}$, let $\mathcal{H}(k)$ be the $d$-partite $d$-uniform hypergraph whose $d$th part has $k$ vertices that share $\mathcal{ H}$ as a common link. We show that $ex(n,\mathcal{H}(k))=Ω_{\mathcal{ H}}(n^{d-\frac{1}{e(\mathcal{H})}})$ if $k$ is at least exponentially large in $e(\mathcal{H})$. Our bound is optimal for all Sidorenko …

On the diagonal of quartic hypersurfaces and $(2,3)$-complete intersection $n$-folds
Elia Fiammengo, Morten L\"uders
https://arxiv.org/abs/2510.07111 https://

On the diagonal of quartic hypersurfaces and $(2,3)$-complete intersection $n$-folds
We study the question of the existence of a decomposition of the diagonal for quartic and $(2,3)$-complete intersection $n$-folds. Using cycle-theoretic techniques of Lange, Pavic and Schreieder we reduce the question via a degeneration argument to the existence of such a decomposition for cubic hypersurfaces and their essential dimension. A result of Voisin on the essential dimension of complex cubic hypersurfaces of odd dimension (and of dimension four) then yields conditional statements that…

On the Jacobian polygon and \L ojasiewicz exponent of isolated complex hypersurface singularities
Baldur Sigur{\dh}sson
https://arxiv.org/abs/2509.06150 https://

On the Jacobian polygon and Łojasiewicz exponent of isolated complex hypersurface singularities
Given a hypersurface singularity $(X,0) \subset (\mathbb{C}^{n+1},0)$ defined by a holomorphic function $f:(\mathbb{C}^{n+1},0) \to (\mathbb{C},0)$, we introduce an alternating version of Teissier's Jacobian Newton polygon, associated with a complex isolated hypersurface singularity, and prove formulas for both these invariants in terms of an embedded resolution of $(X,0)$. The formula for the alternating version has an advantage, in that for Newton nondegenerate functions, it can be calculated…