19 citations · 63 across the 16 of their papers we have counts for
18 papers
Unlabelled Sample Compression Schemes for Intersection-Closed Classes and Extremal Classes
J. Hyam Rubinstein, Benjamin I. P. Rubinstein
The sample compressibility of concept classes plays an important role in learning theory, as a sufficient condition for PAC learnability, and more recently as an avenue for robust…
Counting essential surfaces in 3-manifolds
Nathan M. Dunfield, Stavros Garoufalidis, J. Hyam Rubinstein
We consider the natural problem of counting isotopy classes of essential surfaces in 3-manifolds, focusing on closed essential surfaces in a broad class of hyperbolic 3-manifolds.…
Traversing three-manifold triangulations and spines
J. Hyam Rubinstein, Henry Segerman, Stephan Tillmann
A celebrated result concerning triangulations of a given closed 3-manifold is that any two triangulations with the same number of vertices are connected by a sequence of so-called…
Decomposing Heegaard splittings along separating incompressible surfaces in 3-manifolds
Kazuhiro Ichihara, Makoto Ozawa, J. Hyam Rubinstein
In this paper, by putting a separating incompressible surface in a 3-manifold into Morse position relative to the height function associated to a strongly irreducible Heegaard spli…
Thin position for incompressible surfaces in 3-manifolds
Kazuhiro Ichihara, Makoto Ozawa, J. Hyam Rubinstein
In this paper, we give an algorithm to build all compact orientable atoroidal Haken 3-manifolds with tori boundary or closed orientable Haken 3-manifolds, so that in both cases, th…
Bounding Embeddings of VC Classes into Maximum Classes
J. Hyam Rubinstein, Benjamin I. P. Rubinstein, Peter L. Bartlett
One of the earliest conjectures in computational learning theory-the Sample Compression conjecture-asserts that concept classes (equivalently set systems) admit compression schemes…