Related papers: Tolerance Analysis by Polytopes
In this paper a measure of non-convexity for a simple polygonal region in the plane is introduced. It is proved that for "not far from convex" regions this measure does not decrease under the Minkowski sum operation, and guarantees that the…
The mixed-norm versions of the H\"older and Minkowski integral inequalities are used to produce new, general estimates involving symmetric geometric means of mixed norms. Various existing mixed-norm estimates are shown to be simple special…
The Minkowski problem for a class of unbounded closed convex sets is considered. This is equivalent to a Monge-Amp\`ere equation on a bounded convex open domain with possibly non-integrable given data. A complete solution (necessary and…
We investigate the intersection body of a convex polytope using tools from combinatorics and real algebraic geometry. In particular, we show that the intersection body of a polytope is always a semialgebraic set and provide an algorithm for…
We present an efficient algorithm that computes the Minkowski sum of two polygons, which may have holes. The new algorithm is based on the convolution approach. Its efficiency stems in part from a property for Minkowski sums of polygons…
Tolerance graphs model interval relations in such a way that intervals can tolerate a certain degree of overlap without being in conflict. This subclass of perfect graphs has been extensively studied, due to both its interesting structure…
We study the symplectic geometry of the moduli spaces of polygons in the Minkowski 3-space. These spaces naturally carry completely integrable systems with periodic flows. We extend the Gelfand-Tsetlin method to pseudo-unitary groups and…
Incompressibility is established for three-dimensional and two-dimensional deformations of an anisotropic linearly elastic material, as conditions to be satisfied by the elastic compliances. These conditions make it straightforward to…
The structure of the three-boson bound state in Minkowski space is studied for a model with contact interaction. The Faddeev-Bethe-Salpeter equation is solved both in Minkowski and Euclidean spaces. The results are in fair agreement for…
Determining the number of embeddings of Laman graph frameworks is an open problem which corresponds to understanding the solutions of the resulting systems of equations. In this paper we investigate the bounds which can be obtained from the…
Zonotopes are becoming an increasingly popular set representation for formal verification techniques. This is mainly due to their efficient representation and their favorable computational complexity of important operations in…
We construct and parametrize solutions to the constraint equations of general relativity in a neighborhood of Minkowski spacetime with arbitrary prescribed decay properties at infinity. We thus provide a large class of initial data for the…
We investigate the relationship between stability and the existence of extremal K\"ahler metrics on certain toric surfaces. In particular, we consider how log stability depends on weights for toric surfaces whose moment polytope is a…
Several central problems in quantum information theory (such as measurement compatibility and quantum steering) can be rephrased as membership in the minimal matrix convex set corresponding to special polytopes (such as the hypercube or its…
This paper presents a framework for abstracting uncertain or non-polynomial components of dynamical systems using polynomial constraints. This enables the application of polynomial-based analysis tools, such as sum-of-squares programming,…
Tightness is a generalisation of the notion of convexity: a space is tight if and only if it is "as convex as possible", given its topological constraints. For a simplicial complex, deciding tightness has a straightforward exponential time…
In this paper we investigate the role of symmetry in visual stimuli designed to probe human sensitivity to image statistics. Our starting point is a recently published parameter space, a point in which defines a family of binary texture…
The embedding of a given point set with non-crystallographic symmetry into higher-dimensional space is reviewed, with special emphasis on the Minkowski embedding known from number theory. This is a natural choice that does not require an a…
Given a compact Lagrangian $L$ in a semipositive convex-at-infinity symplectic manifold $W$, we establish a cup-length estimate for the action values of $L$ associated to a Hamiltonian isotopy whose spectral norm is smaller than some…
We approximate boundaries of convex polytopes by smooth hypersurfaces $Y=Y_\varepsilon$ with {\it positive mean curvatures} and, by using basic geometric relations between the scalar curvatures of Riemannin manifolds and the mean curvatures…