We introduce two-player games which build words over infinite alphabets, and we study the problemof checking the existence of winning strategies. These games are played by two players, who take turns inchoosing valuations for variables ranging over an infinite data domain, thus generating multi-attributeddata words. The winner of the game is specified by formulas in the Logic of Rep...

We present two approximate Minkowski sum algorithms for planar regions bounded by line and circle segments. Both algorithms form a convolution curve, construct its arrangement, and use winding numbers to identify sum cells. The first uses the kinetic convolution and the second uses our monotonic convolution. The asymptotic running times of the exact algorithms are increased by km logm with m th...

In this paper we introduce a decision procedure for the combined theory of sets, arithmetic and sums of sets, that can be used as abstraction for problems in verification. This theory and the developed decision procedures is also the first step in our path to develop decision procedures for more theories that can be used as abstraction in more situations, for example with the additional bridgin...

Objective(s): The present study aims to evaluate the protective effect of the compounds isolated from Echinophora cinerea (E. cinerea) against oxidative stress and apoptosis induced by cisplatin (CIS) in PC12 cells. Materials and Methods: Six compounds were isolated as quercetrin-3-O-β-D-glucopyranoside (QUE), osthol (OST), verbenone-5-O-β-D-glycopyranoside (VER), Isoimperatorin (ISO), kaempfer...

Objectives To evaluate clinical characteristics in patients with JIA registered in the hospital based registry. Methods The registry is based on written informed consent. JIA patients were classified using ICD-10 codes and they were registered once. Gender, date of registration and year for disease onset was recorded, in addition to onset type, number of active joints and physician’s global ass...

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 ...

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...