Problem of defining convexity of a digital region is considered. Definition of DL− (digital line) convexity is proposed, and it is shown to be stronger than the other two definitions, T−(triangle) convexity and L−(line) convexity. In attempt to connect the convexity of digital sets, to the fact that digital set can be a fuzzy set, the notion of convexity of the membership function is introduced...

A highway H is a line in the plane on which one can travel at a greater speed than in the remaining plane. One can choose to enter and exit H at any point. The highway time distance between a pair of points is the minimum time required to move from one point to the other, with optional use of H. The highway hull H(S,H) of a point set S is the minimal set containing S as well as the shortest pat...

Consider the classification task of assigning a test object to one of two or more possible groups, or classes. An intuitive way to proceed is to assign the object to that class, to which the distance is minimal. As a distance measure to a class, we propose here to use the distance to the convex hull of that class. Hence the name Nearest Convex Hull (NCH) classification for the method. Convex-hu...

Given a set P of n data points and an integer k, fundamental computational task is to find smaller subset Q⊆P only k which approximately preserves the geometry P. Here we consider problem finding Q best captures convex hull P, where our error measure sum distances in Q. We generalize allow R that must select from differ as well more general functions uncovered such other norms or weighted dista...

We implement the finite-difference (FD) solver and the Hull-White (HW) tree for numerical treatment of the pricing problem under the Hull-White interest rate model. We find that the FD solver is superior to the HW tree.

Recently there has been growing interest among psychologists in human performance on the Euclidean Traveling Salesperson problem (E-TSP). A debate has been initiated on what strategy people use in solving visually presented E-TSP instances. The most prominent hypothesis is the convex-hull hypothesis, originally proposed by MacGregor and Ormerod (1996). We argue that, in the literature so far, t...