Robust positively invariant (RPI) sets for linear difference inclusions are considered here under the assumption that the linear difference inclusion is absolutely asymptotically stable in the absence of additive state disturbances, which is the case for parametrically uncertain or switching linear discrete-time systems controlled by a stabilizing linear state feedback controller. The existence...

The present review deals with the preparation and the properties of star-shaped conjugated compounds. Three, four or six conjugated arms are attached to crossconjugated cores, which consist of single atoms (B, C, N), benzene or azine rings or polycyclic ring systems, as for example triphenylene or tristriazolotriazine. Many of these shape-persistent [n]star compounds tend to -stacking and self...

We introduce k-star-shaped polygons, polygons for which there exists at least one point x such that for any point y of the polygon, segment xy crosses the polygon’s boundary at most k times. The set of all such points x is called the k-kernel of the polygon. We show that the maximum complexity (number of vertices) of the k-kernel of an n-vertex polygon is Θ(n) if k = 2 and Θ(n) if k ≥ 4. We giv...

We consider an optimization version of the image segmentation problem, in which we are given a grid graph with weights on the grid cells. We are interested in finding the maximum weight subgraph such that the subgraph can be decomposed into two ”star-shaped” images. We show that this problem can be reduced to the problem of finding a maximum-weight closed set in an appropriately defined directe...

One of the mantras risk measurement is avoidance concentration. However, most formal approaches to topic actually require more than this. In “Star-Shaped Risk Measures,” Castagnoli, Cattelan, Maccheroni, Tebaldi, and Wang study this property “in purity” for monetary measures. They show that it unites value at convex measures, amenable aggregation opinions, leads treatable optimization, thanks a...

We present a simple algorithm for complete motion planning using deterministic sampling. Our approach relies on computing a star-shaped roadmap of the free space. We partition the free space into star-shaped regions such that a single point called the guard can see every point in the starshaped region. The resulting set of guards capture the intraregion connectivity. We capture the inter-region...