Concept

Regular 4-polytope

Related publications (23)

Robust numerical integration on curved polyhedra based on folded decompositions

Annalisa Buffa, Pablo Antolin Sanchez, Xiaodong Wei

We present a novel method to perform numerical integration over curved polyhedra enclosed by high-order parametric surfaces. Such a polyhedron is first decomposed into a set of triangular and/or rectangular pyramids, whose certain faces correspond to the g ...

ELSEVIER SCIENCE SA2022

An unrefinement algorithm for planar THB-spline parameterizations

Annalisa Buffa

Unrefinement is a tool that allows to perform faster numerical simulations by controlling the level of precision in the specified area. We introduce an algorithm that creates a coarser geometry from an initial regular geometry, which is represented with re ...

ELSEVIER2022

The uniform symbolic topology property for diagonally F-regular algebras

Javier Alonso Carvajal Rojas

Let k be a field of positive characteristic. Building on the work of the second named author, we define a new class of k-algebras, called diagonally F-regular algebras, for which the so-called Uniform. Symbolic Topology Property (USTP) holds effectively. W ...

2020

Capture zone models of a multi-well system in aquifers bounded with regular and irregular inflow boundaries

David Andrew Barry, Setareh Nagheli

Being bounded by hydrological (inflow and barrier) boundaries, natural aquifers have regular/irregular shapes. Here, we consider aquifers bounded by segmental inflow (variable head) boundaries in which water is extracted/injected by a multi-well system. St ...

2020

Presymplectic convexity and (ir)rational polytopes

Tudor Ratiu

In this paper, we extend the Atiyah-Guillemin-Sternberg convexity theorem and Delzant's classification of symplectic toric manifolds to presymplectic manifolds. We also define and study the Morita equivalence of presymplectic toric manifolds and of their c ...

2019

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

Particle size selection in capillary instability of locally heated coaxial fiber

François Gallaire, Pierre-Thomas Paul Brun, Saviz Mowlavi, Isha Shukla

Harnessing fluidic instabilities to produce structures with robust and regular properties has recently emerged as a new fabrication paradigm. This approach is exemplified in the work of Gumennik et al. [Nat. Commun. 4, 2216 (2103)], in which the authors fa ...

AMER PHYSICAL SOC2019

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

The mixing time of the Dikin walk in a polytope-A simple proof

Nisheeth Vishnoi

We study the mixing time of the Dikin walk in a polytope a random walk based on the log-barrier from the interior point method literature. This walk, and a close variant, were studied by Narayanan (2016) and Kannan-Narayanan (2012). Bounds on its mixing ti ...

Elsevier Science Bv2016

Listening to Distances and Hearing Shapes : Inverse Problems in Room Acoustics and Beyond

Ivan Dokmanic

A central theme of this thesis is using echoes to achieve useful, interesting, and sometimes surprising results. One should have no doubts about the echoes' constructive potential; it is, after all, demonstrated masterfully by Nature. Just think about the ...

EPFL2015

Solvability analysis and numerical approximation of linearized cardiac electromechanics

Alfio Quarteroni, Ricardo Esteban Ruiz Baier

This paper is concerned with the mathematical analysis of a coupled elliptic–parabolic system modeling the interaction between the propagation of electric potential and subsequent deformation of the cardiac tissue. The problem consists in a reaction–diffus ...

World Scientific Publ Co Pte Ltd2015

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

Acoustic Echoes Reveal Room Shape

Martin Vetterli, Yue Lu, Ivan Dokmanic, Reza Parhizkar, Andreas Walther

Imagine that you are blindfolded inside an unknown room. You snap your fingers and listen to the room’s response. Can you hear the shape of the room? Some people can do it naturally, but can we design computer algorithms that hear rooms? We show how to com ...

National Academy of Sciences2013

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