Results 11 to 20 of about 2,436 (140)
Discrete & Computational Geometry, 2017 We introduce and study a family of polytopes which can be seen as a generalization of the permutahedron of type $B_d$. We highlight connections with the largest possible diameter of the convex hull of a set of points in dimension $d$ whose coordinates ...
Deza, Antoine +2 more
core +5 more sources
Quadratic Zonotopes:An extension of Zonotopes to Quadratic Arithmetics [PDF]
, 2015 Affine forms are a common way to represent convex sets of $\mathbb{R}$ using a base of error terms $\epsilon \in [-1, 1]^m$. Quadratic forms are an extension of affine forms enabling the use of quadratic error terms $\epsilon_i \epsilon_j$.
Adjé, Assalé +2 more
core +3 more sources
Polar Root Polytopes that are Zonotopes
, 2015 Let $\mathcal P_{\Phi}$ be the root polytope of a finite irreducible crystallographic root system $\Phi$, i.e., the convex hull of all roots in $\Phi$. The polar of $\mathcal P_{\Phi}$, denoted $\mathcal P_{\Phi}^*$, coincides with the union of the orbit
Cellini, Paola, Marietti, Mario
core +4 more sources
Constrained polynomial zonotopes [PDF]
Acta Informatica, 2023 AbstractWe introduce constrained polynomial zonotopes, a novel non-convex set representation that is closed under linear map, Minkowski sum, Cartesian product, convex hull, intersection, union, and quadratic as well as higher-order maps. We show that the computational complexity of the above-mentioned set operations for constrained polynomial zonotopes
Niklas Kochdumper, Matthias Althoff
openaire +3 more sources
Discrete & Computational Geometry, 2023 Abstract We study deformations of graphical zonotopes. Deformations of the classical permutahedron (which is the graphical zonotope of the complete graph) have been intensively studied in recent years under the name of generalized permutahedra.
Padrol, Arnau +2 more
openaire +4 more sources
EXTERNAL ZONOTOPAL ALGEBRA [PDF]
Journal of Algebra and Its Applications, 2013 Zonotopal algebra studies pairs of dual algebraic structures that are associated with a linear matroid X and are connected to corresponding dual geometries. Both the geometry and the algebra encode in their statistics combinatorial properties of the matroid.
Li, Nan, Ron, Amos
openaire +3 more sources
Scalable Zonotope-Ellipsoid Conversions using the Euclidean Zonotope Norm [PDF]
2020 American Control Conference (ACC), 2020 Set-based computations become increasingly popular for safety-critical systems to ensure properties of controllers and observers. To efficiently compute various set operations, one often uses different set representations and conversions between them.
Gasmann, Victor, Althoff, Matthias
openaire +1 more source
Novel Techniques for a Verified Simulation of Fractional-Order Differential Equations
Fractal and Fractional, 2021 Verified simulation techniques have been investigated intensively by researchers who are dealing with ordinary and partial differential equations. Tasks that have been considered in this context are the solution to initial value problems and boundary ...
Andreas Rauh, Luc Jaulin
doaj +1 more source
Zonotopes with Large 2D-Cuts [PDF]
Discrete & Computational Geometry, 2008 minor changes; 14 pages, 7 figures; to appear in Discrete and Computational ...
Rörig, Thilo +2 more
openaire +2 more sources
Fault Detection of Wind Turbines with Uncertain Parameters: A Set-Membership Approach
Energies, 2012 In this paper a set-membership approach for fault detection of a benchmark wind turbine is proposed. The benchmark represents relevant fault scenarios in the control system, including sensor, actuator and system faults.
Thomas Bak +3 more
doaj +1 more source