Three researchers making a material difference.

We study the problem of covering Rd by overlapping translates of a convex polytope, such that almost every point of Rd is covered exactly k times. Such a covering of Euclidean space by a discrete set of translations is called a k-tiling. The investigation of simple tilings by translations (which we call 1-tilings in this context) began with the work of Fedorov [5] and Minkowski [15], and was la...

The experimental design of many micropuncture studies requires clhanges in the perittll)lllar environrment. C'lassically, these clhanges are incluced by systemic infusion of suitable solutions. This technique lhas significant slhortcomings due to the tunavoidlable modification in the composition of the glomertular filtrate an(i to clhanges in the rate of glomerular filtration. Various approachi...

This paper describes the configuration of a floor-tile installation robot for commercial buildings. The research is motivated by the need to reduce the installation time and cost while guaranteeing consistent quality. In order to compete with human installation, a time of 24 seconds per installed tile has to be matched. The technical solution that is deemed feasible and capable of reducing this...

Several applications such as multiprojector displays and microscopy require the mosaicing of images (tiles) acquired by a camera as it traverses an unknown trajectory in 3D space. A homography relates the image coordinates of a point in each tile to those of a reference tile provided the 3D scene is planar. Our approach in such applications is to first perform pairwise alignment of the tiles th...

We consider the problem of building approximate squares in the standard Tile Assembly Model. Given any ε ∈ (0, 1 4 ] we show how to construct squares whose sides are within (1 ± ε)N of any given positive integer N using O ( log 1 ε log log 1 ε + log log εN log log log εN ) tile types. We prove a matching lower bound by showing that Ω ( log 1 ε log log 1 ε + log log εN log log log εN ) tile type...

We prove that the number of tile types required to build squares of size n× n, in Winfree’s abstract Tile Assembly Model, when restricted to using only non-cooperative tile bindings, is at least 2n− 1, which is also the best known upper bound. Non-cooperative self-assembly, also known as “temperature 1”, is where tiles bind to each other if they match on one or more sides, whereas in cooperativ...

In this paper, a subtractive clustering fuzzy identification method and a Sugeno-type fuzzy inference system are used to monitor tile defects in tile manufacturing process. The models for the tile defects are identified by using the firing mechanical resistance, water absorption, shrinkage, tile thickness, dry mechanical resistance and tiles temperature as input data, and using the concavity de...

We settle a number of questions in variants of Winfree’s abstract Tile Assembly Model (aTAM), a model of molecular algorithmic self-assembly. In the “hierarchical” aTAM, two assemblies, both consisting of multiple tiles, are allowed to aggregate together, whereas in the “seeded” aTAM, tiles attach one at a time to a growing assembly. Adleman, Cheng, Goel, and Huang (Running Time and Program Siz...