Concept

Complex polytope

Related publications (21)

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Collapse-invariant properties of spaces equipped with signals or directions

Stefania Ebli

Collapsing cell complexes was first introduced in the 1930's as a way to deform a space into a topological-equivalent subspace with a sequence of elementary moves. Recently, discrete Morse theory techniques provided an efficient way to construct deformatio ...

EPFL2022

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

On the Volume of the John-Lowner Ellipsoid

Grigory Ivanov

We find an optimal upper bound on the volume of the John ellipsoid of a k-dimensional section of the n-dimensional cube, and an optimal lower bound on the volume of the Lowner ellipsoid of a projection of the n-dimensional cross-polytope onto a k-dimension ...

SPRINGER2020

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

Reinforcement learning: the effect of environment

Michael Herzog, He Xu

Reinforcement learning is a type of supervised learning, where reward is sparse and delayed. For example in chess, a series of moves is made until a sparse reward (win, loss) is issued, which makes it impossible to evaluate the value of a single move. Stil ...

2016

Finite Volume Particle Method for Fluid-Structure Interaction

François Avellan, Ebrahim Jahanbakhsh, Audrey Paulette Solange Maertens, Christian Vessaz

We have recently developed a conservative ﬁnite volume particle method (FVPM) that can efﬁciently model 2-D and 3-D ﬂuid ﬂow with free-surfaces and complex geometries. Tn this paper we present an extension of the method to ﬂuid-structure interaction. A new ...

2015

On Polygons Excluding Point Sets

Radoslav Fulek, Balázs Keszegh, Filip Moric

By a polygonization of a finite point set S in the plane we understand a simple polygon having S as the set of its vertices. Let B and R be sets of blue and red points, respectively, in the plane such that is in general position, and the convex hull of B c ...

Springer Japan2013

Representing complex urban geometries in mesoscale modeling

Darren Robinson, Alain Clappier, Adil Rasheed

Real cities are comprised of a diverse, random arrangement of building positions, shapes, and sizes. Yet most of the urban parameterisations thus far developed share the assumption that a city is made up of either a regular array of parallelepipeds or infi ...

2011

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

Origami - geometry of folded plate structures

Yves Weinand, Hans Ulrich Buri

This research proposes new methods to generate rapidly complex folded plate structures that can be built with cross laminated timber panels. Composition and dimensions of these panels as well as the possibility to mill them by Computer Numerically Controll ...

CRC Press/Balkema Taylor & Francis Group2010