Results 51 to 60 of about 14,067 (220)
Journal of the London Mathematical Society, 2019 Let $\text{Tr}(n,m,k)$ denote the largest number of distinct projections onto $k$ coordinates guaranteed in any family of $m$ binary vectors of length $n$. The classical Sauer-Perles-Shelah Lemma implies that $\text{Tr}(n, n^r, k) = 2^k$ for $k \le r$. While determining $\text{Tr}(n,n^r,k)$ precisely for general $k$ seems hopeless even for constant $r$,
Noga Alon, Guy Moshkovitz, Noam Solomon
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Advanced Intelligent Discovery, EarlyView.This article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Yiming Ren, Guo‐Wei Wei
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Hypergraph models of metabolism [PDF]
, 2014 In this paper, we employ a directed hypergraph model to investigate the extent to which environmental variability influences the set of available biochemical reactions within a living cell.
Crofts, JJ, Chuzhanova, N, Pearcy, N
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Hypergraph Diffusions and Resolvents for Norm-Based Hypergraph Laplacians [PDF]
, 2023 The development of simple and fast hypergraph spectral methods has been hindered by the lack of numerical algorithms for simulating heat diffusions and computing fundamental objects, such as Personalized PageRank vectors, over hypergraphs. In this paper,
Tani, Erasmo +4 more
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Humanities & Social Sciences CommunicationsHigher-order relationships exist widely across different disciplines. In the realm of real-world systems, significant interactions involving multiple entities are common.
Bodian Ye +7 more
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On Planar Supports for Hypergraphs
Journal of Graph Algorithms and Applications, 2011 A graph G is a support for a hypergraph H = (V, S) if the vertices of G correspond to the vertices of H such that for each hyperedge Si ∈ S the subgraph of G induced by Si is connected. G is a planar support if it is a support and planar.
Kevin Buchin +4 more
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On partitioning of hypergraphs
Discrete Mathematics, 2007 The edge-isoperimetric problem on graphs (EIP), namely for a given integer \(m\) and graph \(G=(V,E)\) to find a subset \(A\) of the vertices of \(G\) of cardinality \(m\) so that the number of edges of \(G\) connecting vertices in \(A\) to vertices in \(V\setminus A\), is minimized (version 1), or such that the number of edges of \(G\) induced by \(A\)
S. Bezrukov, Battiti, Roberto
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Density Conditions for k $k$ Vertex‐Disjoint Triangles in Tripartite Graphs
Journal of Graph Theory, EarlyView.ABSTRACT Let n , k $n,k$ be positive integers such that n ≥ k $n\ge k$ and G $G$ be a tripartite graph with parts A , B , C $A,B,C$ such that ∣ A ∣ = ∣ B ∣ = ∣ C ∣ = n $| A| =| B| =| C| =n$. Denote the edge densities of G [ A , B ] , G [ A , C ] $G[A,B],G[A,C]$ and G [ B , C ] $G[B,C]$ by α , β $\alpha ,\beta $ and γ $\gamma $, respectively.
Mingyang Guo, Klas Markström
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Directed hypergraph neural network [PDF]
, 2022 To deal with irregular data structure, graph convolution neural networks have been developed by a lot of data scientists. However, data scientists just have concentrated primarily on developing deep neural network method for un-directed graph.
Tran, Linh Hoang, Tran, Loc Hoang
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Combinatorics, Probability and ComputingAbstract For $\ell \geq 3$ , an $\ell$
Lior Gishboliner, Ethan Honest
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