Toric codes are evaluation codes obtained from an integral convex polytope P ⊂ R and finite field Fq. They are, in a sense, a natural extension of Reed-Solomon codes, and have been studied recently in [6], [8], [9], and [12]. In this paper, we obtain upper and lower bounds on the minimum distance of a toric code constructed from a polygon P ⊂ R by examining Minkowski sum decompositions of subpo...

This paper proposes a fast algorithm for implementing the basic operation of Minkowski addition for the special case of binary three-dimensional images, using three-dimensional structuring elements of arbitrary size and shape. The application of the proposed algorithm for all the other morphological transformations is straightforward, as they can all be expressed in terms of Minkowski addition....

The parameters ∆H R, ∆S ◦ R and ∆Cp can all be calculated from knowledge of various changes in accessible surface area (ASA), which is defined as the surface traced out by a sphere, with radius equal to that of a solvent molecule, when rolled over the surface of the molecule of interest. This can also be formulated in configuration space as the Minkowski sum of the protein and the sphere, namel...

The original definition of P-systems calls for rules to be applied in a maximally parallel fashion. However, in some cases a sequential model may be a more reasonable assumption. Here we study the computational power of different variants of sequential P-systems. Initially we look at cooperative systems operating on symbol objects and without prioritized rules, but which allow membrane dissolut...

This article reports the use of a karaoke technique to drive the visual attention span (VAS) of subjects reading a text while listening to the text spelled aloud by a reading tutor. We tested the impact of computer-assisted synchronous reading (S+) that emphasizes words when they are uttered, vs. non-synchronous reading (S-) in a reading while listening (RWL) task. Thirty-five 6th grade pupils ...

The combinatorial complexities of (1) the Voronoi diagram of moving points in 2D and (2) the Voronoi diagram of lines in 3D, both under the Euclidean metric, continues to challenge geometers because of the open gap between the (n2) lower bound and the O(n3+ε) upper bound. Each of these two combinatorial problems has a closely related problem involving Minkowski sums: (1′) the complexity of a Mi...

Majority of the advances in spectacle lens continue to occur in the area of progressive lens design by most of the spectacle lens manufacturers. Since the introduction of progressive addition lenses (PALs) in 1959 by Essilor, it has gained worldwide acceptance for the treatment of presbyopia. While progressive lens design, manufacturing and dispensing techniques have grown at a good pace in the...

This papers shows that using separators, which is a pair of two complementary contractors, we can easily and efficiently solve the localization problem of a robot with sonar measurements in an unstructured environment. We introduce separators associated with the Minkowski sum and the Minkowski difference in order to facilitate the resolution. A test-case is given in order to illustrate the prin...