An N-tiling of triangle ABC by triangle T (the “tile”) is a way of writing ABC as a union of N copies of T overlapping only at their boundaries. We continue the work of [1, 2] on classifying the possible triangle tilings. The results of all three papers together enable us to make some progress on two problems of Erdős about triangle tilings, one of which asks, “for which N is there an N-tiling ...

Tiling is widely used by compilers and programmer to optimize scientific and engineering code for better performance. Many parallel programming languages support tile/tiling directly through first-class language constructs or library routines. However, the current OpenMP programming language is tile oblivious, although it is the de facto standard for writing parallel programs on shared memory s...

Jingling Xue Department of Mathematics, Statistics and Computing Science University of New England, Armidale 2351, Australia ABSTRACT This paper is a follow-up to Irigoin and Triolet's earlier work and our recent work on tiling. In this paper, tiling is discussed in terms of its e ects on the dependences between tiles, the dependenceswithin a tile and the required dependence test for legality. ...

This paper describes the development of a modular system of interactive tiles to support therapists’ in performing therapeutic activities together with impaired children in a swimming pool. This work is based upon a deep understanding of therapist work practice and it has been integrated with a creative approach along iterative design cycles. These activities created the foundation on which the...

Ceramic floor tile systems can provide a durable finish; however, if internal stresses are allowed to accumulate in the tile system, fractured, buckled, and/or hollow-sounding tiles may develop. Using case studies of residential structures, this paper will discuss common perils that cause damage to ceramic floor tile systems and how these perils can be avoided through proper installation and ma...

In large and continuous state-action spaces reinforcement learning heavily relies on function approximation techniques. Tile coding is a well-known function approximator that has been successfully applied to many reinforcement learning tasks. In this paper we introduce the hyperplane tile coding, in which the usual tiles are replaced by parameterized hyperplanes that approximate the action-valu...

images divided into independent tiles in the pixel domain is important. However, tiling introduces artifacts when transform coefficients are quantized. This paper presents a " detiling " solution applicable to wavelet transform coefficients. The solution, called Projection Onto Scaling Functions, eliminates the blocking artifacts by computing approximations that match the smoothness of the comp...

In this paper we formalize the concept of square tiles with colored corners, a new kind of tiles closely related to Wang tiles. We construct aperiodic sets of square tiles with colored corners and several new aperiodic sets of Wang tiles using isomorphisms between tilings. The smallest aperiodic set of square tiles with colored corners we have created consists of 44 tiles over 6 colors.

ACKNOWLEDGEMENTS First of all, I would like to express my special and sincere gratitude to my advisor Dr. George Vachtsevanos for his persistent guidance and trust throughout my research. His enthusiasm for the career affected me greatly. I would also like to thank my co-advisor Dr. Bonnie Heck-Ferri and Wayne Daley, my project supervisor, for their support and technical discussions. Secondly, ...

We introduce and study the number of tilings of unit height rectangles with irrational tiles. We prove that the class of sequences of these numbers coincides with the class of diagonals of N-rational generating functions and a class of certain binomial multisums. We then give asymptotic applications and establish connections to hypergeometric functions and Catalan numbers.