We study the convex hull of the intersection of a convex set E and a disjunctive set. This intersection is at the core of solution techniques for Mixed Integer Convex Optimization. We prove that if there exists a cone K (resp., a cylinder C) that has the same intersection with the boundary of the disjunction as E , then the convex hull is the intersection of E with K (resp., C). The existence o...

Although many cyber-physical systems are both mixed-criticality system and compositional system, there are little work on intersection of mixed-criticality system and compositional system. We propose novel concepts for task-level criticality mode and reconsider temporal isolation in terms of compositional mixed-criticality scheduling.

This paper addresses the problem of obtaining a consistent estimate (or upper bound) of the covariance matrix when combining two quantities with unknown correlation. The combination is defined linearly with two gains. When the gains are chosen a priori, a family of consistent estimates is presented in the paper. The member in this family having minimal trace is said to be “family-optimal”. When...

Let g1, . . . , gk be tropical polynomials in n variables with Newton polytopes P1, . . . , Pk. We study combinatorial questions on the intersection of the tropical hypersurfaces defined by g1, . . . , gk, such as the f -vector, the number of unbounded faces and (in case of a curve) the genus. Our point of departure is Vigeland’s work [33] who considered the special case k = n− 1 and where all ...

In [Kol00], A. Koldobsky asked whether two types of generalizations of the notion of an intersection-body, are in fact equivalent. The structures of these two types of generalized intersection-bodies have been studied in [Mil06b], providing substantial positive evidence for a positive answer to this question. The purpose of this note is to construct a counter-example, which provides a surprisin...

Let t(C) be the number of tangent pairs among a set C of n Jordan regions in the plane. Pach, Suk, and Treml [6] showed that if C consists of convex bodies and its intersection graph is bipartite then t(C) ≤ 4n−Θ(1), and, moreover, there are such sets that admit at least 3n−Θ( √ n) tangencies. We close this gap and generalize their result by proving that the correct bound is 3n−Θ(1), even when ...