… Affine forms define zonotopes in higher dimensions, which means that the complexity of
geometric algorithms (which use the points or faces of the region) grows exponentially in the …

The halfspace depth of a point p relative to a data set S in d-dimension is the smallest
number of data observations from S in any closed halfspace containing p. A point with largest …

… We can now forget about linear transformations (they are performed on constant complexity
sets) We should focus on Minkowski sum: s we can use Zonotopes [Girard] time complexity …

We study the q-state Potts model with nearest-neighbor coupling v=e βJ −1 in the limit q,v →
0 with the ratio w = v/q held fixed. Combinatorially, this limit gives rise to the generating …

… The encoding and representation methods described in the core of the paper seem really
promissing, and we expect new results for a larger class of zonotopes, and for tilings of more …

We will show how a variety of interval algorithms have found their use in the multibody
modeling program MOBILE. This paper acquaints the reader with the key features of this open …

The directional measure (which is up to normalization the rose of directions) is used to quantify
anisotropy of stationary fibre processes in three‐dimensional space. There exist a large …

We discuss how well a given convex body B in a real d-dimensional vector space V can be
approximated by a set X for which the membership question: ``given an x in V, does x belong …

The cd-index is a polynomial which encodes the flag f-vector of a convex polytope. For
polytopes U and V, we determine explicit recurrences for computing the cd-index of the free join \…

… for examples ellip soids [9, 16, 53, 82], zonotopes [1, 31] and parallelotopes [17] to define a
… Zonotopes and parallelotopes are special polytopes and this speciality makes them not as …