Compressed Genotyping

Significant volumes of knowledge have been accumulated in recent years linking subtle genetic variations to a wide variety of medical disorders from Cystic Fibrosis to mental retardation. Nevertheless, there are still great challenges in applying this knowledge routinely in the clinic, largely due to the relatively tedious and expensive process of DNA sequencing. Since the genetic polymorphisms that underlie these disorders are relatively rare in the human population, the presence or absence of a disease-linked polymorphism can be thought of as a sparse signal. Using methods and ideas from compressed sensing and group testing, we have developed a cost-effective genotyping protocol. In particular, we have adapted our scheme to a recently developed class of high throughput DNA sequencing technologies, and assembled a mathematical framework that has some important distinctions from 'traditional' compressed sensing ideas in order to address different biological and technical constraints.Comment: Submitted to IEEE Transaction on Information Theory - Special Issue on Molecular Biology and Neuroscienc

Non-adaptive pooling strategies for detection of rare faulty items

We study non-adaptive pooling strategies for detection of rare faulty items. Given a binary sparse N-dimensional signal x, how to construct a sparse binary MxN pooling matrix F such that the signal can be reconstructed from the smallest possible number M of measurements y=Fx? We show that a very low number of measurements is possible for random spatially coupled design of pools F. Our design might find application in genetic screening or compressed genotyping. We show that our results are robust with respect to the uncertainty in the matrix F when some elements are mistaken.Comment: 5 page

Detection and Mapping of Quantitative Trait Loci that Determine Responsiveness

Exposure to 70% N2O evokes a robust antinociceptive effect in C57BL/6 (B6) but not in DBA/2 (D2) inbred mice. This study was conducted to identify quantitative trait loci (QTL) in the mouse genome that might determine responsiveness to N2O. Offspring from the F2 generation bred from B6 and D2 progenitors exhibited a broad range of responsiveness to N2O antinociception as determined by the acetic acid-induced abdominal constriction test. QTL analysis was then used to dissect this continuous trait distribution into component loci, and to map them to broad chromosomal regions. To this end, 24 spleens were collected from each of the following four groups: male and female F2 mice responding to 70% N2O in oxygen with 100% response (high-responders); and male and female F2 mice responding with 0% response (low-responders). Genomic DNA was extracted from the spleens and genotyped with simple sequence length polymorphism MapPairs markers. Findings were combined with findings from the earlier QTL analysis from BXD recombinant inbred mice [Brain Res 725 (1996) 23]. Combined results revealed two significant QTL that influence responsiveness to nitrous oxide on proximal chromosome 2 and distal chromosome 5, and one suggestive QTL on midchromosome 18. The chromosome 2 QTL was evident only in males. A significant interaction was found between a locus on chromosome 6 and another on chromosome 13 with a substantial effect on N2O antinociception

Mixed Operators in Compressed Sensing

Applications of compressed sensing motivate the possibility of using different operators to encode and decode a signal of interest. Since it is clear that the operators cannot be too different, we can view the discrepancy between the two matrices as a perturbation. The stability of L1-minimization and greedy algorithms to recover the signal in the presence of additive noise is by now well-known. Recently however, work has been done to analyze these methods with noise in the measurement matrix, which generates a multiplicative noise term. This new framework of generalized perturbations (i.e., both additive and multiplicative noise) extends the prior work on stable signal recovery from incomplete and inaccurate measurements of Candes, Romberg and Tao using Basis Pursuit (BP), and of Needell and Tropp using Compressive Sampling Matching Pursuit (CoSaMP). We show, under reasonable assumptions, that the stability of the reconstructed signal by both BP and CoSaMP is limited by the noise level in the observation. Our analysis extends easily to arbitrary greedy methods.Comment: CISS 2010 (44th Annual Conference on Information Sciences and Systems