In this paper, we introduce the notion of a constrained Minkowski sum which for two (finite) point-sets P,Q ⊆ R2 and a set of k inequalities Ax > b is defined as the point-set (P⊕Q)Ax>b = {x = p+q | p ∈ P, q ∈ Q, Ax > b}. We show that typical interval problems from computational biology can be solved by computing a set containing the vertices of the convex hull of an appropriately constrained M...

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...

In this short communication, we observe that the Graphical Traveling Salesman Polyhedron is the intersection of the positive orthant with the Minkowski sum of the Symmetric Traveling Salesman Polytope and the polar of the metric cone. This follows trivially from known facts. There are two reasons why we find this observation worth communicating none-the-less: It is very surprising; it helps to ...

In this paper we consider the problem of computing control invariant sets for linear controlled systems with constraints on the input and on the states. We focus in particular on the complexity of the computation of the N-step operator, given by the Minkowski addition of sets, that is the basis of many of the iterative procedures for obtaining control invariant sets. Set inclusions conditions f...

Tropical geometry is used to develop a new approach to the theory of discriminants and resultants in the sense of Gel'fand, Kapranov and Zelevinsky. The tropical A-discriminant, which is the tropicalization of the dual variety of the projective toric variety given by an integer matrix A, is shown to coincide with the Minkowski sum of the row space of A and the tropicalization of the kernel of A...