This work presents a study of two image registration methods for ceramic tile inspection purposes. Tile registration is the first step in detecting surface faults when a ‘compare with a reference’ technique is used. The presented methods are based on edge detection techniques, used to extract the bounding rectangle defined by the tiles. They differ in the approach used to obtain this rectangle....

Let b ≥ 2 be an integer base, D = {0, d1, · · · , db−1} ⊂ Z a digit set and T = T (b,D) the set of radix expansions. It is well known that if T has nonvoid interior, then T can tile R with some translation set J (T is called a tile and D a tile digit set). There are two fundamental questions studied in the literature: (i) describe the structure of J ; (ii) for a given b, characterize D so that ...

2-categories and double categories are respectively the natural semantic ground for rewriting logic (rl) and tile logic (tl). Since 2-categories can be regarded as a special case of double categories, then rl can be easily embedded into tl, where also rewriting synchronization is considered. Since rl is the semantic basis of several existing languages, it is useful to map tl back into rl to hav...

A web geographical information system is a typical service-intensive application. Tile prefetching and cache replacement can improve cache hit ratios by proactively fetching tiles from storage and replacing the appropriate tiles from the high-speed cache buffer without waiting for a client's requests, which reduces disk latency and improves system access performance. Most popular prefetching st...

We extend the study of Akiyama’s tile-makers: surfaces whose developments all tile the plane. First, we prove that the developments of Akiyama’s tile-makers are the prototiles that tile the plane isohedrally with rotation and without reflection. Second, we give a simple characterization of all closed (boundaryless) tile-makers and give three new tile-makers not known to Akiyama. Finally, we pro...

We show that the Tile Assembly Model exhibits a strong notion of universality where the goal is to give a single tile assembly system that simulates the behavior of any other tile assembly system. We give a tile assembly system that is capable of simulating a very wide class of tile systems, including itself. Specifically, we give a tile set that simulates the assembly of any tile assembly syst...

Self-assembly is a process found everywhere in the Nature. In particular, it is known that DNA self-assembly is Turing universal. Thus one can do arbitrary computations or build nano-structures using DNA self-assembly. In order to understand the DNA self-assembly process, many mathematical models have been proposed in the literature. In particular, abstract Tile Assembly Model (aTAM) received m...

Self-assembly is the process whereby relatively simple components autonomously combine to form more complex objects. Nature exhibits self-assembly to form everything from microscopic crystals to living cells to galaxies. With a desire to both form increasingly sophisticated products and to understand the basic components of living systems, scientists have developed and studied artificial self-a...

DNA Self-Assembly has emerged as an interdisciplinary field with many intriguing applications such DNA bio-sensor, DNA circuits, DNA storage, drug delivery etc. Tile assembly model of DNA has been studied for various computational primitives such as addition, subtraction, multiplication, and division. Xuncai et. al. gave computational DNA tiles to perform division of a number but the output had...

1T HE DUMBELL-DIFFUSION CELL described by Nobel (1) is made from a ball and socket joint, each end of which is formed into a bell-shaped flask. This cell is applicable to rapid testing of blood for the presence or absence of various toxic constituents. it allows diffusion, absorption, and i(lentiflcation reactions to proceed concurrently under a variety of conditions (Table 1). [sing this appar...