This paper studies the composition operator for credal sets introduced at the last ISIPTA conference in more detail. Our main attention is devoted to the relationship between a special type of compositional model, so-called perfect sequences of credal sets, and those of (precise) probability distributions, with the goal of finding the relationship between credal compositional models and credal ...

If X is a vector space and E is a subset of X, the convex hull of E is defined to be the intersection of all convex sets containing E, and is denoted by co(E). One checks that the convex hull of E is equal to the set of all finite convex combinations of elements of E. If X is a topological vector space, the closed convex hull of E is the intersection of all closed convex sets containing E, and ...

Let K be a smooth convex set with volume one in R. Choose n random points in K independently according to the uniform distribution. The convex hull of these points, denoted by Kn, is called a random polytope. We prove that several key functionals of Kn satisfy the central limit theorem as n tends to infinity.

Let X be a normed linear space. We investigate properties of vector functions F : [a, b] → X of bounded convexity. In particular, we prove that such functions coincide with the delta-convex mappings admitting a Lipschitz control function, and that convexity K aF is equal to the variation of F ′ + on [a, b). As an application, we give a simple alternative proof of an unpublished result of the fi...

Closure spaces have been previously investigated by Paul Edelman and Robert Jami-son as \convex geometries". Consequently, a number of the results given here duplicate theirs. However, we employ a slightly diierent, but equivalent, deening axiom which gives a new avor to our presentation. The major contribution is the deenition of a partial order on all subsets, not just closed (or convex) subs...

The tropical convex hull of a finite set of points in tropical projective space has a natural structure of a cellular free resolution. Therefore, methods from computational commutative algebra can be used to compute tropical convex hulls. This approach is computationally competitive with combinatorial methods. Tropical cyclic polytopes are also presented.

Let K be a smooth convex set. The convex hull of independent random points in K is a random polytope. Central limit theorems for the volume and the number of i dimensional faces of random polytopes are proved as the number of random points tends to infinity. One essential step is to determine the precise asymptotic order of the occurring variances.

We introduce a novel representation of classifier conditions based on convex hulls. A classifier condition is represented by a sets of points in the problem space. These points identify a convex hull that delineates a convex region of the problem space. The condition matches all the problem instances inside such region. We apply XCSF with convex conditions to function approximation problems and...

The Q-convexity is a kind of convexity in the discrete plane. This notion has practically the same properties as the usual convexity: an intersection of two Qconvex sets is Q-convex, and the salient points can be defined like the extremal points. Moreover a Q-convex set is characterized by its salient point. The salient points can be generalized to any finite subset of Z2.

K. S. Lau had shown that a reflexive Banach space has the Mazur Intersection Property (MIP) if and only if every closed bounded convex set is the closed convex hull of its farthest points. In this work, we show that in general this latter property is equivalent to a property stronger than the MIP. As corollaries, we recapture the result of Lau and characterize the w*-MIP in dual of RNP spaces.