Surface fitting methods play an important role in many scientific fields as well as in computer aided geometric design. The problem treated here is that of constructing a smooth surface that interpolates data values associated with scattered nodes in the plane. The data is said to be convex if there exists a convex interpolant. The problem of convexity-preserving interpolation is to determine if the data is convex, and construct a convex interpolant if it exists.

DNA sequence analysis involves precise discrimination of two of the sequence's most important components: exons and introns. Exons encode the proteins that are responsible for almost all the functions in a living organism. Introns interrupt the sequence coding for a protein and must be removed from primary RNA transcripts before translation to protein can occur. A pattern recognition technique called Finite Induction (FI) is utilized to study the language of exons and introns. FI is especially suited for analyzing and classifying large amounts of data representing sequences of interest. It requires no biological information and employs no statistical functions. Finite Induction is applied to the exon and intron components of DNA by building a collection of rules based upon what it finds in the sequences it examines. It then attempts to match the known rule patterns with new rules formed as a result of analyzing a new sequence. A high number of matches predict a probable close relationship between the two sequences; a low number of matches signifies a large amount of difference between the two. This research demonstrates FI to be a viable tool for measurement when known patterns are available for the formation of rule sets.

A useful compiler has been designed that takes a high level neural network specification and constructs a low level configuration file explicitly specifying all network parameters and connections. The neural network model for which this compiler was designed is the adaptrode neuronal model, and the configuration file created can be used by the Adnet simulation engine to perform network experiments. The specification language is very flexible and provides a general framework from which almost any network wiring configuration may be created. While the compiler was created for the specialized adaptrode model, the wiring specification algorithms could also be used to specify the connections in other types of networks.

The goal of a parallel algorithm is to solve a single problem using multiple processors working together and to do so in an efficient manner. In this regard, there is a need to categorize strategies in order to solve broad classes of problems with similar structures and requirements. In this dissertation, two parallel algorithm design strategies are considered: linked list ranking and parentheses matching.

The scope of the present dissertation is a deep lossy compression of still and moving grayscale pictures while maintaining their fidelity, with a specific goal of creating a working prototype of a software system for use in low bandwidth transmission of still satellite imagery and weather briefings with the best preservation of features considered important by the end user.

The motivation behind this research has been the idea of the capability of the computing device to dynamically reconfigure itself. The goal of this work is to measure the computational power of reconfigurable machines rather in an abstract manner by proposing a model the FPGAs abstract computing machines. Modeling FPGAs in terms of Automata Theory would give a base to answer more fundamental questions about the capabilities and possible answers. If a Finite State Machine (FSM) or a Turing Machine (TM) has the capability of reconfiguring its finite control, does this ability give the abstract computing device new computational power. In other words is a reconfigurable FSM, TM or a Cellular Automata more powerful than their corresponding non-configurable versions?