Mathematics
Permanent URI for this communityhttp://hdl.handle.net/1903/2261
Browse
2 results
Search Results
Item Novel Methods for Metagenomic Analysis(2010) White, James Robert; Pop, Mihai; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)By sampling the genetic content of microbes at the nucleotide level, metagenomics has rapidly established itself as the standard in characterizing the taxonomic diversity and functional capacity of microbial populations throughout nature. The decreasing cost of sequencing technologies and the simultaneous increase of throughput per run has given scientists the ability to deeply sample highly diverse communities on a reasonable budget. The Human Microbiome Project is representative of the flood of sequence data that will arrive in the coming years. Despite these advancements, there remains the significant challenge of analyzing massive metagenomic datasets to make appropriate biological conclusions. This dissertation is a collection of novel methods developed for improved analysis of metagenomic data: (1) We begin with Figaro, a statistical algorithm that quickly and accurately infers and trims vector sequence from large Sanger-based read sets without prior knowledge of the vector used in library construction. (2) Next, we perform a rigorous evaluation of methodologies used to cluster environmental 16S rRNA sequences into species-level operational taxonomic units, and discover that many published studies utilize highly stringent parameters, resulting in overestimation of microbial diversity. (3) To assist in comparative metagenomics studies, we have created Metastats, a robust statistical methodology for comparing large-scale clinical datasets with up to thousands of subjects. Given a collection of annotated metagenomic features (e.g. taxa, COGs, or pathways), Metastats determines which features are differentially abundant between two populations. (4) Finally, we report on a new methodology that employs the generalized Lotka-Volterra model to infer microbe-microbe interactions from longitudinal 16S rRNA data. It is our hope that these methods will enhance standard metagenomic analysis techniques to provide better insight into the human microbiome and microbial communities throughout our world. To assist metagenomics researchers and those developing methods, all software described in this thesis is open-source and available online.Item Anomaly Detection in Time Series: Theoretical and Practical Improvements for Disease Outbreak Detection(2009) Lotze, Thomas Harvey; Shmueli, Galit; Applied Mathematics and Scientific Computation; Digital Repository at the University of Maryland; University of Maryland (College Park, Md.)The automatic collection and increasing availability of health data provides a new opportunity for techniques to monitor this information. By monitoring pre-diagnostic data sources, such as over-the-counter cough medicine sales or emergency room chief complaints of cough, there exists the potential to detect disease outbreaks earlier than traditional laboratory disease confirmation results. This research is particularly important for a modern, highly-connected society, where the onset of disease outbreak can be swift and deadly, whether caused by a naturally occurring global pandemic such as swine flu or a targeted act of bioterrorism. In this dissertation, we first describe the problem and current state of research in disease outbreak detection, then provide four main additions to the field. First, we formalize a framework for analyzing health series data and detecting anomalies: using forecasting methods to predict the next day's value, subtracting the forecast to create residuals, and finally using detection algorithms on the residuals. The formalized framework indicates the link between the forecast accuracy of the forecast method and the performance of the detector, and can be used to quantify and analyze the performance of a variety of heuristic methods. Second, we describe improvements for the forecasting of health data series. The application of weather as a predictor, cross-series covariates, and ensemble forecasting each provide improvements to forecasting health data. Third, we describe improvements for detection. This includes the use of multivariate statistics for anomaly detection and additional day-of-week preprocessing to aid detection. Most significantly, we also provide a new method, based on the CuScore, for optimizing detection when the impact of the disease outbreak is known. This method can provide an optimal detector for rapid detection, or for probability of detection within a certain timeframe. Finally, we describe a method for improved comparison of detection methods. We provide tools to evaluate how well a simulated data set captures the characteristics of the authentic series and time-lag heatmaps, a new way of visualizing daily detection rates or displaying the comparison between two methods in a more informative way.