In this thesis, we propose a systematic code for correcting t = 1 insertion/deletion errors of the character ”0” that can occur between any two consecutive 1’s in a binary string. The code requires balanced input strings, where each word of length n contains ⌈n/2⌉ 0’s and ⌊n/2⌋ 1’s. This...
We define an inner product on a vector space of adelic measures over a number field $K$. We find that the norm induced by this inner product governs weak convergence at each place of $K$. The canonical adelic measure associated to a rational map is in this vector space, and...
Recent advances in computing, communication, and artificial intelligence (AI) technologies have made our world more interconnected and data-rich than ever with the proliferation of smart devices and sensors. As a result, we are increasingly dependent on electronic devices and sensors to automate away life’s mundane parts. For example, in business...
Iterative algorithms are simple yet efficient in solving large-scale optimization problems in practice. With a surge in the amount of data in past decades, these methods have become increasingly important in many application areas including matrix/tensor recovery, deep learning, data mining, and reinforcement learning. To optimize or improve iterative algorithms,...
NAND flash based solid state drives (SSDs) require out-of-place updating due to the characteristics of flash memories. In addition, due to the mismatched granularity between read/write and erase operations, a cleaning policy involving garbage collection and wear leveling has to perform data migration incurring high overhead. Another challenge is that...