A receiver operating characteristic (ROC) curve is a plot of predictive model probabilities of true positives (sensitivity) as a function of probabilities of false positives (1 – specificity) for a set of possible cutoff points. Some of the SAS/STAT procedures do not have built-in options for ROC curves and there have been a few suggestions in previous SAS forums to address the issue by using e...

We propose a new nite cone covering algorithm for concave minimization over a polytope, in which the cones are de ned by extreme points of the polytope. The main novelties are the use of cones de ned by an arbitrary number of edges, and the subdivision process. This latter is shown to have a \descent property", i.e., all subcones are strictly better in some sense than the subdivided cone, which...

A well know conjecture states that the Whitney numbers of the second kind of a geometric lattice (simple matroid) are logarithmically concave. We show this conjecture to be equivalent to proving an upper bound on the number of new copoints in the free erection of the associated simple matroid M . A bound on the number of these new copoints is given in terms of the copoints and colines of M . Al...

The Shape From Shading is one of a computer vision field. It studies the 3D reconstruction of an object from a single grayscale image. The difficulty of this field can be expressed in the local ambiguity (convex / concave). J.Shi and Q.Zhu have proposed a method (Global View) to solve the local ambiguity. This method based on the graph theory and the relationship between the singular points. In...

We investigate the problem of designing a minimum cost flow network interconnecting n sources and a single sink, each with known locations and flows. The network may contain other unprescribed nodes, known as Steiner points. For concave increasing cost functions, a minimum cost network of this sort has a tree topology, and hence can be called a Minimum Gilbert Arborescence (MGA). We characteris...

This paper is concerned with the study of necessary and sufficient optimality conditions for convex–concave generalized fractional disjunctive programming problems for which the decision set is the union of a family of convex sets. The Lagrangian function for such problems is defined and the Kuhn–Tucker Saddle and Stationary points are characterized. In addition, some important theorems related...

We investigate the extremal points of a functional ∫ f(∇u), for a convex or concave function f . The admissible functions u : Ω ⊂ RN → R are convex themselves and satisfy a condition u2 ≤ u ≤ u1. We show that the extremal points are exactly u1 and u2 if these functions are convex and coincide on the boundary ∂Ω. No explicit regularity condition is imposed on f , u1, or u2. Subsequently we discu...