Omnibus Sequences, Coupon Collection, and Missing Word Counts

An {\it Omnibus Sequence} of length $n$ is one that has each possible "message" of length $k$ embedded in it as a subsequence. We study various properties of Omnibus Sequences in this paper, making connections, whenever possible, to the classical coupon collector problem.Comment: 26 page

Analysis of high-depth sequence data for studying viral diversity: a comparison of next generation sequencing platforms using Segminator II

Background: Next generation sequencing provides detailed insight into the variation present within viral populations, introducing the possibility of treatment strategies that are both reactive and predictive. Current software tools, however, need to be scaled up to accommodate for high-depth viral data sets, which are often temporally or spatially linked. In addition, due to the development of novel sequencing platforms and chemistries, each with implicit strengths and weaknesses, it will be helpful for researchers to be able to routinely compare and combine data sets from different platforms/chemistries. In particular, error associated with a specific sequencing process must be quantified so that true biological variation may be identified. Results: Segminator II was developed to allow for the efficient comparison of data sets derived from different sources. We demonstrate its usage by comparing large data sets from 12 influenza H1N1 samples sequenced on both the 454 Life Sciences and Illumina platforms, permitting quantification of platform error. For mismatches median error rates at 0.10 and 0.12%, respectively, suggested that both platforms performed similarly. For insertions and deletions median error rates within the 454 data (at 0.3 and 0.2%, respectively) were significantly higher than those within the Illumina data (0.004 and 0.006%, respectively). In agreement with previous observations these higher rates were strongly associated with homopolymeric stretches on the 454 platform. Outside of such regions both platforms had similar indel error profiles. Additionally, we apply our software to the identification of low frequency variants. Conclusion: We have demonstrated, using Segminator II, that it is possible to distinguish platform specific error from biological variation using data derived from two different platforms. We have used this approach to quantify the amount of error present within the 454 and Illumina platforms in relation to genomic location as well as location on the read. Given that next generation data is increasingly important in the analysis of drug-resistance and vaccine trials, this software will be useful to the pathogen research community. A zip file containing the source code and jar file is freely available for download from http://www.bioinf.manchester.ac.uk/segminator/

Predicting Extreme Returns and Portfolio Management Implications

We consider which readily observable characteristics of individual stocks (e.g., option implied volatility, accounting data, analyst data) may be used to forecast subsequent extreme price movements. We are the first to explicitly consider the predictive influence of option implied volatility in such a framework, which we unsurprisingly find to be an important indicator of future extreme price movements. However, after controlling for implied volatility levels, other factors, particularly firm age and size, still have additional predictive power of extreme future returns. Furthermore, excluding predicted extreme return stocks leads to a portfolio that has lower risk (standard deviation of returns) without sacrificing performance