PURPOSE This study was performed to determine the optimal tile size for the fractal dimension of the mandibular trabecular bone using a tile counting method. MATERIALS AND METHODS Digital intraoral radiographic images were obtained at the mandibular angle, molar, premolar, and incisor regions of 29 human dry mandibles. After preprocessing, the parameters representing morphometric characterist...

Experiments have demonstrated that DNA molecules can compute like a machine to solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical reactions, DNA computation suffers from errors, which are its main limitation. The abstract and kinetic Tile Assembly Models are now commonly used to simulate real DNA computing e...

We discuss the self-assembly system of triangular tiles instead of square tiles, in particular right triangular tiles and equilateral triangular tiles. We show that the triangular tile assembly system, either deterministic or non-deterministic, has the same power to the square tile assembly system in computation, which is Turing universal. By providing counter-examples, we show that the triangu...

The cracking and subsequent fallout of glazing could significantly affect the dynamics of fires in compartments. The sudden venting resulting from the fallout of a window glass may result in backdraft or flashover depending on the development stage of the fire. The need for research on glazing behaviour in fires was first identified by Emmons [1]. There are two main physical processes involved ...

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...

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...

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.