In this thesis we study self-assembly systems, in particular, we focus on the tile complexity of shapes. Using the standard tile assembly model proposed by Rothemund and Winfree, we give two lower bounds on the tile complexity of arbitrary shapes in terms of the radius and diameter of the shape. Applying our results to a square yields a partial answer to a problem of Rothemund and Winfree. We a...

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...

Majumder, Reif and Sahu presented in [11] a model of reversible, errorpermitting tile self-assembly, and showed that restricted classes of tile assembly systems achieved equilibrium in (expected) polynomial time. One open question they asked was how the model would change if it permitted multiple nucleation, i.e., independent groups of tiles growing before attaching to the original seed assembl...

Subsurface tile drains in agricultural systems of the midwestern United States are a major contributor of nitrate-N (NO-N) loadings to hypoxic conditions in the Gulf of Mexico. Hydrologic and water quality models, such as the Soil and Water Assessment Tool, are widely used to simulate tile drainage systems. The Hooghoudt and Kirkham tile drain equations in the Soil and Water Assessment Tool hav...

The tile assembly model has allowed the study of the nature’s process of self-assembly and the development of self-assembling systems for solving complex computational problems. Research into this model has led to progress in two distinct classes of computational systems: Internet-sized distributed computation, such as software architectures for computational grids, and molecular computation, s...

We present an algorithm for compressing pattern databases (PDBs) and a method for fast random access of these compressed PDBs. We demonstrate the effectiveness of our technique by compressing two 6-tile sliding-tile PDBs by a factor of 12 and a 7-tile sliding-tile PDB by a factor of 24.