Rate-Optimal Detection of Very Short Signal Segments

Detection of very short signal segments arise in a wide range of applications in many fields including engineering, genomics, and material science. For example, copy number variations (CNVs) play a significant role in the genetics of complex disease. Therefore the detection of CNVs due to duplication and deletion of a segment of DNA sequences is an important problem in genomics. In contrast to single-nucleotide polymorphisms which affects only one single nucleotide base, each CNV corresponds to a short segment of the genome, typically around 1000 nucleotide bases, that has been altered (see, e.g., Stankiewicz and Lupski, 2010). Although the length of these CNVs is much smaller than that of the whole genome, recognizing and accounting for such segment structure are critical in effective detection of CNVs (see, e.g., Jeng, Cai and Li, 2010).