Tootfinder

Domination, matching and transversal numbers for Berge-$G$ hypergraphs
Mar\'ia Jos\'e Ch\'avez de Diego, Pablo Montero Moreno, Mar\'ia Trinidad Villar-Li\~n\'an
https://arxiv.org/abs/2507.22957

Domination, matching and transversal numbers for Berge-$G$ hypergraphs
Let $G=(V(G),E(G))$ be a graph and $H=(V(H),E(H))$ be a hypergraph. The hypergraph $H$ is a {\it Berge-G} if there is a bijection $f : E(G) \mapsto E(H)$ such that for each $e \in E(G)$ we have $e \subseteq f(e)$. We define {\it dilations of $G$} as a particular subfamily of not necessarily uniform Berge-$G$ hypergraphs. We examine domination, matching and transversal numbers and some relation between these parameters in that family of hypergraphs. Our work generalizes previous results concer…

Hypergeometric Local Systems and Parabolic Bundles
Charlie Wu
https://arxiv.org/abs/2509.25629 https://arxiv.org/pdf/2509.25629

Hypergeometric Local Systems and Parabolic Bundles
Beukers and Heckman gave necessary and sufficient conditions for a hypergeometric function $_n F_{n-1}$ to be algebraic. We give a new proof of this theorem by passing through the Mehta-Seshadri correspondence. In particular, we explicitly write down the parabolic bundle corresponding to a unitary hypergeometric local system.

8 coax lanes, DC - 70 GHz, solderless compression fit... *drool*
https://www.hubersuhner.com/en/newsroom/blog-and-literature/blog/introducing-mxpd70-the-next-step-in-multicoax-test-solut…

Networked Physical Computing: A New Paradigm for Effective Task Completion via Hypergraph Aided Trusted Task-Resource Matching
Botao Zhu, Xianbin Wang
https://arxiv.org/abs/2507.23556

Networked Physical Computing: A New Paradigm for Effective Task Completion via Hypergraph Aided Trusted Task-Resource Matching
Due to the diverse physical attributes of computing resources and tasks, developing effective mechanisms to facilitate task and resource matching in complex connected systems for value-oriented task completion has become increasingly challenging. To address the challenge, this paper proposes a networked physical computing system that integrates the physical attributes of computing resources and tasks as well as task-specific trust relationships among devices to enable value-driven task completi…

Upper tails for homomorphism counts in sparse random hypergraphs
Nicholas A. Cook, Nguyen Nguyen
https://arxiv.org/abs/2509.26569 https://arxiv.org/pdf/250…

Upper tails for homomorphism counts in sparse random hypergraphs
The "infamous upper tail problem" for $r$-uniform hypergraphs is to estimate the probability that the number of copies of a fixed hypergraph $H$ in a large binomial $r$-uniform hypergraph $\boldsymbol{G}$ exceeds its expectation by a constant factor. The problem was popularized by Janson and Ruciński and, particularly in the case of graphs ($r=2$), has been a driving example in the development of nonlinear large deviations theory. Recent work of the first author with Dembo and Pham has accompl…

An SoS Entropy Dichotomy via Windowed Hypercontractivity
Marko Lela
https://arxiv.org/abs/2509.24280 https://arxiv.org/pdf/2509.24280

An SoS Entropy Dichotomy via Windowed Hypercontractivity
We prove an entropy versus degree dichotomy for low-degree tests and the Sum-of-Squares (SoS) hierarchy on a calibrated window after a gadget layer. For a target distribution \(μ\) and a product-like proxy \(u\), we study the low-degree discrepancy \(Δ_k(μ,u)\), defined as the optimal distinguishing advantage of degree \(\le k\) polynomial tests. Using a bias-orthonormal Walsh basis and a test-moment equivalence on the window, we relate \(Δ_k\) (up to constants) to the squared \(\ell_2\) ma…

Structure-aware Hypergraph Transformer for Diagnosis Prediction in Electronic Health Records
Haiyan Wang, Ye Yuan
https://arxiv.org/abs/2508.20500 https://…

Structure-aware Hypergraph Transformer for Diagnosis Prediction in Electronic Health Records
Electronic Health Records (EHR) systematically organize patient health data through standardized medical codes, serving as a comprehensive and invaluable source for predictive modeling. Graph neural networks (GNNs) have demonstrated effectiveness in modeling interactions between medical codes within EHR. However, existing GNN-based methods are inadequate due to: a) their reliance on pairwise relations fails to capture the inherent higher-order dependencies in clinical data, and b) the localized…

Dyadic Neural Dynamics: Extending Representation Learning to Social Neuroscience
Maria Glushanina, Jeffrey Huang, Michelle McCleod, Brendan Ames, Evie Malaia
https://arxiv.org/abs/2509.23479

Dyadic Neural Dynamics: Extending Representation Learning to Social Neuroscience
Social communication fundamentally involves at least two interacting brains, creating a unique modeling problem. We present the first application of Contrastive Embedding for Behavioral and Neural Analysis (CEBRA) to dyadic EEG hyperscanning data, extending modeling paradigms to interpersonal neural dynamics. Using structured social interactions between participants, we demonstrate that CEBRA can learn meaningful representations of joint neural activity that captures individual roles (speaker-l…

Hodge Conjecture via Singular Varieties
Ananyo Dan, Inder Kaur
https://arxiv.org/abs/2509.25273 https://arxiv.org/pdf/2509.25273

Hodge Conjecture via Singular Varieties
In this article we study the cohomological and homological (due to Jannsen) Hodge conjecture for singular varieties. The motivation for studying singular varieties comes from the fact that any smooth projective variety X is birational to a (possibly singular) hypersurface Y in a projective space. We prove that odd dimensional hypersurfaces with $A_n$ singularities satisfy both versions of the conjecture and moreover their (smooth) resolutions satisfy the classical Hodge conjecture, thus produci…

On the Chromatic Number of Stable Kneser Hypergraphs: Verifying the Conjecture for New Families
Hamid Reza Daneshpajouh
https://arxiv.org/abs/2509.22026 https://

On the Chromatic Number of Stable Kneser Hypergraphs: Verifying the Conjecture for New Families
One of the key unsolved conjectures in hypergraph coloring is about the chromatic number of $s$-stable $r$-uniform Kneser hypergraphs $\mathrm{KG}^r(n,k)_{s\textup{-stab}}$. The problem remains largely open, particularly in the case where $s > r\geq 3$. To the best of our knowledge, no information is available except a limited number of computations conducted for the instances when $r=3, 4$, $s=4, 5$, $k=2,3$ with some $n$ does not exceed 14. In this study, we verify the conjecture for infinity…