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Machine learning predictions from unpredictable chaos. [PDF]

J R Soc Interface
Jiang J, Chen L, Ke L, Dou B, Zhu Y, Shi Y, Qiu H, Zhang BG, Zhou T, Wei GW.   +9 more
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Regularity Lemma for k‐uniform hypergraphs

Random Structures & Algorithms, 2004
AbstractSzemerédi's Regularity Lemma proved to be a very powerful tool in extremal graph theory with a large number of applications. Chung [Regularity lemmas for hypergraphs and quasi‐randomness, Random Structures Algorithms 2 (1991), 241–252], Frankl and Rödl [The uniformity lemma for hypergraphs, Graphs Combin 8 (1992), 309–312; Extremal problems on ...
Rödl, Vojtěch, Skokan, Jozef
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An Algorithmic Regularity Lemma for Hypergraphs

SIAM Journal on Computing, 2000
Szemerédi's seminal ``regularity lemma'' is a powerful tool in extremal combinatorics and graph theory. Its algorithmic version (due to Alon et al.) has important applications to construct effective algorithms. This long and technically hard paper develops an analogous result for hypergraphs (which differs from other, earlier versions).
Czygrinow, Andrzej, Rödl, Vojtech
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List Colourings of Regular Hypergraphs

Combinatorics, Probability and Computing, 2012
We show that the list chromatic number of a simpled-regularr-uniform hypergraph is at least (1/2rlog(2r2) +o(1)) logdifdis large.
DAVID SAXTON, ANDREW THOMASON
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Hypergraph regularized sparse feature learning

Neurocomputing, 2017
As an important pre-processing stage in many machine learning and pattern recognition domains, feature selection deems to identify the most discriminate features for a compact data representation. As typical feature selection methods, Lasso and its variants using the l1-norm based regularization have received much attention in recent years.
Mingxia Liu, Jun Zhang, Xiaochun Guo, Liujuan Cao   +3 more
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Extending regular edge‐colorings of complete hypergraphs

Journal of Graph Theory, 2019
AbstractA coloring (partition) of the collection of all ‐subsets of a set is ‐regular if the number of times each element of appears in each color class (all sets of the same color) is the same number . We are interested in finding the conditions under which a given ‐regular coloring of is extendible to an ‐regular coloring of for and . The case
Amin Bahmanian, Sadegheh Haghshenas
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Regular Representation of Finite Groups by Hypergraphs

Canadian Journal of Mathematics, 1978
All structures considered in this paper will be finite.The product στ of two permutations σ and τ of a set V is defined by στ(x) = στ(X)) for every x ∈ V. The set Sv of all permutations of F is a group under this operation. A permutation group on F is a subgroup of Sv.
Foldes, Stephane, Singhi, Navin M.
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Regularity lemmas for hypergraphs and quasi‐randomness

Random Structures & Algorithms, 1991
AbstractWe give a simple proof for Szemerédi's Regularity Lemma and its generalization for k‐uniform hypergraphs. For fixed k, there are altogether k ‐1 different versions of the regularity lemma for k‐uniform hypergraphs. The connection between regularity lemmas for hypergraphs and quasi‐random classes of hypergraphs is also investigated.
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Equivalent regular partitions of three‐uniform hypergraphs

Random Structures & Algorithms
AbstractThe regularity method was pioneered by Szemerédi for graphs and is an important tool in extremal combinatorics. Over the last two decades, several extensions to hypergraphs were developed which were based on seemingly different notions of quasirandom hypergraphs.
Nagle, Brendan, Rödl, Vojtěch, Schacht, Mathias   +2 more
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Emerging Technologies in Screening for Colorectal Cancer: CT Colonography, Immunochemical Fecal Occult Blood Tests, and Stool Screening Using Molecular Markers

Ca-A Cancer Journal for Clinicians, 2003
Robert A Smith
exaly