This work presents a novel technique for data compression based on multi-residue number systems. The basic theorem is that an under-determined system of congruences could be solved to accomplish data compression for a signal satisfying continuity of its information content and bounded in peak-to -peak amplitude by the product of relatively prime moduli,. This thesis investigates this property and presents quantitative results along with MATLAB codes. Chapter 1 is introductory in nature and Chapter 2 deals in more detail with the basic theorem. Chapter 3 explicitly mentions the assumptions made and chapter 4 shows alternative solutions to the Chinese remainder theorem. Chapter 5 explains the experiments in detail whose results are mentioned in chapter 6. Chapter 7 concludes with a summary and suggestions for future work.

Network structure plays a significant role in determining the performance of network inference tasks. An interactive tool to study the dependence of network topology on estimation performance was developed. The tool allows end-users to easily create and modify network structures and observe the performance of pole estimation measured by Cramer-Rao bounds. The tool also automatically suggests the best measurement locations to maximize estimation performance, and thus finds its broad applications on the optimal design of data collection experiments. Finally, a series of theoretical results that explicitly connect subsets of network structures with inference performance are obtained.