We introduce a novel method for constructing polyhedra by blending together two or more existing polyhedra, using a dualization method. The method results in a Minkowski sum, analogous to that of overlay tilings [5], which uses a topological dual operation to create tilings from a network (a graph embedded in a plane). This paper extends that method to networks on the surface of the unit sphere...

Let X1, . . . , XN denote N independent d-dimensional Lévy processes, and consider the N -parameter random field X(t) := X1(t1) + · · ·+XN (tN ). First we demonstrate that for all nonrandom Borel sets F ⊆ R, the Minkowski sum X(R+ ) ⊕ F , of the range X(R+ ) of X with F , can have positive d-dimensional Lebesgue measure if and only if a certain capacity of F is positive. This improves our earli...

By extending former results of Ehrhart, it was shown by Peter McMullen that the number of lattice points in the Minkowski-sum of dilated rational polytopes is a quasipolynomial function in the dilation factors. Here we take a closer look at the coefficients of these quasi-polynomials and show that they are piecewise polynomials themselves and that they are related to each other by a simple diff...

The vertices of the secondary polytope of a point connguration correspond to its regular triangulations. The Cayley trick links triangulations of one point connguration, called the Cayley polytope, to the ne mixed subdivisions of a tuple of point conngurations. In this paper we investigate the secondary polytope of this Cayley polytope. Its vertices correspond to all regular mixed subdivisions ...

We consider here a variation of Vector Addition Systems where one counter can be tested for zero, extending the reachability proof by Leroux for Vector Addition System to our model. This provides an alternate, and hopefully simpler to understand, proof of the reachability problem that was originally proved by Reinhardt.

Method We used 3112 16-year-olds from a Swedish birth cohort called BAMSE. The adolescents who fulfilled the criteria of CRS according to the European Position Paper on Rhinosinusitis (EPOS) in a questionnaire, was contacted by telephone to verify the diagnosis. Those with ongoing symptoms were invited for a clinical follow up with nasal endoscopy, olfactory threshold test (Sniffin’ sticks) and...

Participants decided whom of two patients to prioritize for surgery in three studies. The factual quantitative information about the patients (e.g., probability of surviving surgery) was given in vignette form with case descriptions on Visual Analogue Scales — VAS’s. Differentiation and Consolidation theory predicts that not only the attractiveness of facts but also the mental representations o...

Reachability and boundedness problems have been shown decidable for Vector Addition Systems with one zero-test. Surprisingly, place-boundedness remained open. We provide here a variation of the Karp-Miller algorithm to compute a basis of the downward closure of the reachability set which allows to decide place-boundedness. This forward algorithm is able to pass the zero-tests thanks to a finer ...

This paper proposes a fast algorithm for implementing the basic operation of Minkowski addition for the special case of binary three-dimensional (3-D) images, using 3-D structuring elements of arbitrary size and shape. The application of the proposed algorithm for all the other morphological transformations is straightforward, as they can all be expressed in terms of Minkowski addition. The eff...