Let S be a set of n intervals in R, and let (S,+) be any commutative semigroup. We assign a weight ω(s) ∈ S to each interval in S. For a point x ∈ R, let S(x) ⊆ S be the set of intervals that contain x. Given a point q ∈ R, the stabbing-semigroup query asks for computing

Pulmonary artery dissection is a fatal complication of long-standing pulmonary hypertension, manifesting as acute, stabbing chest pain, progressive dyspnea, cardiogenic shock, or sudden death. Its incidence has been underestimated, and therapeutic options are still scarce. In patients with pulmonary hypertension, new chest pain, acute chest pain, or cardiogenic shock should raise the suspicion ...

We present a deterministic linear time algorithm to find a set of five points that stab a set of n pairwise intersecting disks in the plane. We also give a simple construction with 13 pairwise intersecting disks that cannot be stabbed by three points.

Reports describing traumatic lesions to the heart caused by a foreign body are comparatively rare. Such trauma is often associated with a poor outcome due to injury to the heart or major blood vessels with subsequent massive blood loss. Delayed presentation and intervention are associated with poor outcome in these patients. This report describes a 17-year-old male who presented with stabbing t...

It is shown that for every subdivision of the d-dimensional Euclidean space, d ≥ 2, into n convex cells, there is a straight line that stabs at least Ω((log n/ log log n)1/(d−1)) cells. In other words, if a convex subdivision of d-space has the property that any line stabs at most k cells, then the subdivision has at most exp(O(kd−1 log k)) cells. This bound is best possible apart from a consta...

The following result was proved by Bárány in 1982: For every d ≥ 1 there exists cd > 0 such that for every n-point set S in R d there is a point p ∈ R contained in at least cdn d+1 −O(n) of the d-dimensional simplices spanned by S. We investigate the largest possible value of cd. It was known that cd ≤ 1/(2(d+ 1)!) (this estimate actually holds for every point set S). We construct sets showing ...