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Concept

4-polytope

Related publications (24)

EXISTENCE OF AN UNBOUNDED NODAL HYPERSURFACE FOR SMOOTH GAUSSIAN FIELDS IN DIMENSION d >= 3

Alejandro Rivera

For the Bargmann-Fock field on R-d with d >= 3, we prove that the critical level l(c) (d) of the percolation model formed by the excursion sets {f >= l} is strictly positive. This implies that for every l sufficiently close to 0 (in particular for the noda ...

INST MATHEMATICAL STATISTICS-IMS2023

Reduced representations of complexes, signals, and multifiltrations

Celia Camille Hacker

The field of computational topology has developed many powerful tools to describe the shape of data, offering an alternative point of view from classical statistics. This results in a variety of complex structures that are not always directly amenable for ...

EPFL2022

Promoting Persistent Superionic Conductivity in Sodium Monocarba-closo-dodecaborate NaCB11H12 via Confinement within Nanoporous Silica

Mirjana Dimitrievska

Superionic phases of bulk anhydrous salts based on large cluster-like polyhedral (carba)borate anions are generally stable only well above room temperature, rendering them unsuitable as solid-state electrolytes in energy-storage devices that typically oper ...

AMER CHEMICAL SOC2021

First passage sets of the 2D continuum Gaussian free field

Juhan Aru, Titus Lupu

We introduce the first passage set (FPS) of constant level -a of the two-dimensional continuum Gaussian free field (GFF) on finitely connected domains. Informally, it is the set of points in the domain that can be connected to the boundary by a path on whi ...

SPRINGER HEIDELBERG2020

Tropical Ehrhart Theory and Tropical Volume

Matthias Schymura, Georg Peter Loho

We introduce a novel intrinsic volume concept in tropical geometry. This is achieved by developing the foundations of a tropical analog of lattice point counting in polytopes. We exhibit the basic properties and compare it to existing measures. Our exposit ...

2019

Extended Formulations from Communication Protocols in Output-Efficient Time

Yuri Faenza, Manuel Francesco Aprile

Deterministic protocols are well-known tools to obtain extended formulations, with many applications to polytopes arising in combinatorial optimization. Although constructive, those tools are not output-efficient, since the time needed to produce the exten ...

SPRINGER INTERNATIONAL PUBLISHING AG2019

Deforming Tessellations for the Segmentation of Cell Aggregates

Michaël Unser, Daniel Sage, Aymeric Alexandre Galan, Anaïs Laure Marie-Thérèse Badoual

We present a new active contour to segment cell aggregates. We describe it by a smooth tessellation that is attracted toward the cell membranes. Our approach relies on subdivision schemes that are tightly linked to the theory of wavelets. The shape is enco ...

IEEE2019

On 2-Level Polytopes Arising In Combinatorial Settings

Yuri Faenza, Manuel Francesco Aprile, Alfonso Bolívar Cevallos Manzano

2-level polytopes naturally appear in several areas of pure and applied mathematics, including combinatorial optimization, polyhedral combinatorics, communication complexity, and statistics. In this paper, we present a study of some 2-level polytopes arisi ...

SIAM Publications2018

On some problems related to 2-level polytopes

Manuel Francesco Aprile

In this thesis we investigate a number of problems related to 2-level polytopes, in particular from the point of view of the combinatorial structure and the extension complexity. 2-level polytopes were introduced as a generalization of stable set polytopes ...

EPFL2018

Non-Normal Very Ample Polytopes - Constructions and Examples

Michal Lason

We answer several questions posed by Beck, Cox, Delgado, Gubeladze, Haase, Hibi, Higashitani, and Maclagan in [Cox et al. 14, Question 3.5 (1),(2), Question 3.6], [Beck et al. 15, Conjecture 3.5(a),(b)], and [Hasse et al. 07, Open question 3 (a),(b) p. 231 ...

Taylor & Francis Inc2017

Homogeneous selections from hyperplanes

János Pach

Given d + 1 hyperplanes h(1),..., h(d+1) in general position in R-d, let Delta(h(1),..., h(d+1)) denote the unique bounded simplex enclosed by them. There exists a constant c(d) > 0 such that for any finite families H-1,..., Hd+1 of hyperplanes in R-d, the ...

Academic Press Inc Elsevier Science2014

Comments on: Recent progress on the combinatorial diameter of polytopes and simplicial complexes

Friedrich Eisenbrand

This paper features two main contributions. On the one hand, it gives an impressive survey on the progress on the diameter problem, including the breakthrough of the author with his disproof of the Hirsch conjecture among many other recent results. On the ...

Springer2013

Weakly regular subdivisions

Lionel Pournin

It is shown that 2-dimensional subdivisions can be made regular by moving their vertices within parallel 1-dimensional spaces. As a consequence, any 2-dimensional subdivision is projected from the boundary complex of a 4-polytope. ...

Springer-Verlag2012

Belt distance between facets of space-filling zonotopes

To every d-dimensional polytope P with centrally symmetric facets one can assign a “subway map” such that every line of this “subway” contains exactly the facets parallel to one of the ridges of P. The belt diameter of P is the maximum number of subway lin ...

2012

Étude d'un manuscrit de Ludwig Schläfli - Euklid. 2 Hefte

Rachel Bendjama Faller

The great Swiss mathematician Ludwig Schläfli (1814-1895) left after his death more than three hundred and fifty notebooks. They include mathematical studies and new results, as well as works about classical mathematical texts and a priori more surprising ...

EPFL2011

A linear equation for Minkowski sums of polytopes relatively in general position

Christophe Weibel

The objective of this paper is to study a special family of Minkowski sums, that is of polytopes relatively in general position. We show that the maximum number of faces in the sum can be attained by this family. We present a new linear equation that is sa ...

2010

Optimal decision trees for point location in polytopic data sets - application to explicit MPC

Colin Neil Jones

Explicit Model Predictive Control (EMPC) produces control laws defined over a set of polytopic regions in the state space. In this paper we present a method to create a binary search tree for point location in such polytopic sets, in order to provide a fas ...

2010

Propagation and absorption of low frequency waves in two and three dimensional warm plasmas

In order to model a broader range of phenomena taking place in three-dimensional plasmas, the LEMan code has been extended to a warm formulation. As the wave propagation is strongly influenced by the parallel wave vector, special attention has been paid fo ...

EPFL2009

Chiral kagome lattice from simple ditopic molecular bricks

Klaus Kern, Harald Brune, Uta Schlickum, Régis Decker

Self-assembly techniques allow for the fabrication of highly organized architectures with atomic-level precision. Here, we report on molecular-level scanning tunneling microscopy observations demonstrating the supramolecular engineering of complex, regular ...

American Chemical Society2008

Multimodal Distribution of Quantum Confinement in Ripened CdSe Nanocrystals

Majed Chergui, Philip Pattison, Awos Al Salman

We present three different prepn. methods for CdSe colloidal nanoparticles that, when carried out into the Ostwald ripening regime, lead to the development of complex spectral patterns resulting from the overlap of several distinct components corresponding ...

2008