Zobrazeno 1 - 10
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pro vyhledávání: '"Soberón, P."'
Autor:
Sadovek, Nikola, Soberón, Pablo
In this paper, we study a problem of mass partitions by parallel hyperplanes. Takahashi and Sober\'on conjectured an extension of the classical ham sandwich theorem: any $d+k-1$ measures in $\mathbb{R}^d$ can be simultaneously equipartitioned by $k$
Externí odkaz:
http://arxiv.org/abs/2412.04058
Autor:
Sadovek, Nikola, Soberón, Pablo
The Tverberg--Vre\'cica conjecture is a broad generalization of Tverberg's classical theorem. One of its consequences, the central transversal theorem, extends both the centerpoint theorem and the ham sandwich theorem. In this manuscript, we establis
Externí odkaz:
http://arxiv.org/abs/2408.14337
Autor:
Soberón, Pablo
We show how, using linear-algebraic tools developed to prove Tverberg's theorem in combinatorial geometry, we can design new models of multi-class support vector machines (SVMs). These supervised learning protocols require fewer conditions to classif
Externí odkaz:
http://arxiv.org/abs/2404.16724
Autor:
Hubard, Alfredo, Soberón, Pablo
We prove a common generalization to several mass partition results using hyperplane arrangements to split $\mathbb{R}^d$ into two sets. Our main result implies the ham-sandwich theorem, the necklace splitting theorem for two thieves, a theorem about
Externí odkaz:
http://arxiv.org/abs/2404.14320
Autor:
Edwards, Timothy, Soberón, Pablo
We prove extensions of Halman's discrete Helly theorem for axis-parallel boxes in $\mathbb{R}^d$. Halman's theorem says that, given a set $S$ in $\mathbb{R}^d$, if $F$ is a finite family of axis-parallel boxes such that the intersection of any $2d$ c
Externí odkaz:
http://arxiv.org/abs/2404.14308
Autor:
Soberón, Pablo, Zerbib, Shira
A theorem of Gr\"unbaum, which states that every $m$-polytope is a refinement of an $m$-simplex, implies the following generalization of Tverberg's theorem: if $f$ is a linear function from an $m$-dimensional polytope $P$ to $\mathbb{R}^d$ and $m \ge
Externí odkaz:
http://arxiv.org/abs/2404.11533
Autor:
Soberón, Pablo, Yu, Christina
A vast array of envy-free results have been found for the subdivision of one-dimensional resources, such as the interval $[0,1]$. The goal is to divide the space into $n$ pieces and distribute them among $n$ observers such that each receives their fa
Externí odkaz:
http://arxiv.org/abs/2311.09905
Given a finite set of points in $\mathbb{R}^d$, Tverberg's theorem guarantees the existence of partitions of this set into parts whose convex hulls intersect. We introduce a graph structured on the family of Tverberg partitions of a given set of poin
Externí odkaz:
http://arxiv.org/abs/2310.08563
Krasnosselsky's art gallery theorem gives a combinatorial characterization of star-shaped sets in Euclidean spaces, similar to Helly's characterization of finite families of convex sets with non-empty intersection. We study colorful and quantitative
Externí odkaz:
http://arxiv.org/abs/2304.04828
Autor:
Schnider, Patrick, Soberón, Pablo
Regression depth, introduced by Rousseeuw and Hubert in 1999, is a notion that measures how good of a regression hyperplane a given query hyperplane is with respect to a set of data points. Under projective duality, this can be interpreted as a depth
Externí odkaz:
http://arxiv.org/abs/2302.07768