Zobrazeno 1 - 10
of 13
pro vyhledávání: '"Johannes Hofscheier"'
Autor:
Jiakang Bao, Yang-Hui He, Edward Hirst, Johannes Hofscheier, Alexander Kasprzyk, Suvajit Majumder
Publikováno v:
Physics Letters B, Vol 827, Iss , Pp 136966- (2022)
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ∼1 mean absolute error, whilst classifiers predict dimension and Gorenst
Externí odkaz:
https://doaj.org/article/5d1ec6604c1444dca489827bc5b9d8af
Publikováno v:
manuscripta mathematica. 170:147-165
In this paper we motivate some new directions of research regarding the lattice width of convex bodies. We show that convex bodies of sufficiently large width contain a unimodular copy of a standard simplex. This implies that every lattice polytope c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4c6fbb6b93d8c21877e666cc1d70c3da
https://doi.org/10.1007/s00229-021-01363-x
https://doi.org/10.1007/s00229-021-01363-x
Autor:
Victor Batyrev, Johannes Hofscheier
An m-dimensional simplex ? in Rm is called empty lattice simplex if ? ? Zm is exactly the set of vertices of ?. A theorem of White states that if m = 3 then, up to an affine unimodular transformation of the lattice Zm, any empty lattice simplex ? ? R
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::90053797bd69b3533d7b322ff49f6353
https://nottingham-repository.worktribe.com/file/6344106/1/Generalized-Th-White
https://nottingham-repository.worktribe.com/file/6344106/1/Generalized-Th-White
Autor:
Johannes Hofscheier
Publikováno v:
Springer Proceedings in Mathematics & Statistics ISBN: 9783030983260
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::51c3c044267ceed53856516fc849f42b
https://doi.org/10.1007/978-3-030-98327-7_9
https://doi.org/10.1007/978-3-030-98327-7_9
Autor:
Yang-Hui He, Jiakang Bao, Johannes Hofscheier, Suvajit Majumder, Alexander Kasprzyk, Edward Hirst
Publikováno v:
Physics Letters
We describe how simple machine learning methods successfully predict geometric properties from Hilbert series (HS). Regressors predict embedding weights in projective space to ${\sim}1$ mean absolute error, whilst classifiers predict dimension and Go
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bf1dfadcd4fb29d601b8d668b047eced
Let $I \subseteq R = \mathbb{K}[x_1,\ldots,x_n]$ be a toric ideal, i.e., a binomial prime ideal. We investigate when the ideal $I$ can be "split" into the sum of two smaller toric ideals. For a general toric ideal $I$, we give a sufficient condition
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::7f158ea1de06f8cf53f69d1e0e28208a
http://arxiv.org/abs/1909.12820
http://arxiv.org/abs/1909.12820
Autor:
Akihiro Higashitani, Katharina Jochemko, Johannes Hofscheier, Matthias Beck, Christian Haase, Lukas Katthän, Mateusz Michałek
In 1997 Oda conjectured that every smooth lattice polytope has the integer decomposition property. We prove Oda's conjecture for centrally symmetric $3$-dimensional polytopes, by showing they are covered by lattice parallelepipeds and unimodular simp
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5d25df62dbbe9ae90eb3b271c40dbb8e
http://arxiv.org/abs/1802.01046
http://arxiv.org/abs/1802.01046
Autor:
Johannes Hofscheier, Adam Van Tuyl, Craig Kohne, Miguel Eduardo Uribe Paczka, Graham Keiper, Federico Galetto
We compute the graded Betti numbers for the toric ideal of a family of graphs constructed by adjoining a cycle to a complete bipartite graph. The key observation is that this family admits an initial ideal which has linear quotients. As a corollary,
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::a0d8e6cb48fc5a226c038ca571a01a99
Publikováno v:
Transformation Groups. 20:83-98
Let $G$ be a connected reductive complex algebraic group. Luna assigned to any spherical homogeneous space $G/H$ a combinatorial object called a homogeneous spherical datum. By a theorem of Losev, this object uniquely determines $G/H$ up to $G$-equiv
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::53f967d1fed77b5e2f60e2f6c31aaf7c
https://doi.org/10.1007/s00031-014-9297-2
https://doi.org/10.1007/s00031-014-9297-2
A lattice polytope is called spanning if its lattice points affinely span the ambient lattice. We show as a corollary to a general result in the Ehrhart theory of lattice polytopes that the $h^*$-vector of a spanning lattice polytope has no gaps, i.
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::846377f5a93a99ff0906d9f7d83fb356