An Integrated Data Analysis Suite and Programming ... - TOBIAS-lib

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56 CHAPTER 2. A HIGH-THROUGHPUT DNA SEQUENCING DATA ANALYSIS SUITE Depth of Coverage [# Reads] 0 5 10 15 20 25 Median Depth of Coverage Depth Inner Quartiles Average Depth ±SD 2:1 2:10000001 3:200001 3:10200001 3:20200001 Position [bp] Figure 2.10: Segment-Wise Genome-Wide Box Plot is encountered, depth of coverage can be hard to judge from the read alignments alone. Therefore, the SHORE mapdisplay program generates an overlay of depth of coverage, represented as vertical bars, and the horizontal bars of the read mappings. In addition, the SVG view allows retrieval of exact depth of coverage information for each position and detailed alignment information for each of the reads displayed in the form of mouse activated tool tips. 2.8.3 Visualization of Local or Genome-Scale Depth of Coverage SHORE coverage is a multi-purpose tool for depth of coverage calculation and depth based segmentation (section 2.7). The complementary SHORE count utility gathers a wide variety of segmentrelated statistics. Like most SHORE modules, both programs are capable of rapidly retrieving and processing alignment information associated with dened regions of the genome. SHORE coverage can be utilized to obtain visual representations of local depth of coverage (gure 2.6) or of kmer-phasing for small RNA data analysis (not shown). Per-base rendering of depth of coverage is however inappropriate for examination of larger scale distribution of sequencing depth. Visualization capability for such types of analysis is integrated with the SHORE count program. The software collects segment associated statistics for either user provided or xed size jumping window segments. The segment data collected may be incorporated into a continuous genome- or chromosome-wide box plot (gure 2.10). In the representation, the median line connects the median depth of coverage value for each of the segments provided, and is enclosed by boxes indicating second and third quartiles as well as the single standard deviation range surrounding the average depth of coverage of the segment. Red vertical bars indicate chromosome boundaries. As read depths mostly represent integer values, median and quartile values are adjusted to compensate quantization (section 2.8.4).
2.8. VISUALIZATION OF SEQUENCING READ AND ALIGNMENT DATA 57 Quality Score 16 24 32 40 Depth of Coverage [# Reads] 0 5 10 Median Base Quality Inner Quality Quartiles 1 11 21 31 41 51 61 71 81 1 11 21 31 41 51 61 71 81 Cycle [bp] Median Depth of Coverage Depth Inner Quartiles 3:9250001 3:9250001 Position [bp] Figure 2.11: Quantile Interpolation Applied to Base Qualities and to Depth of Coverage 2.8.4 Quantile Correction As in the case of base quality data or positional depth of coverage, quantile values of integer data distributed over a narrow range only coarsely represent the distribution of interest due to the small number of dierent values that such quantiles can assume (gure 2.11, left side). Given that the integer data in fact represent real-valued entities that have at some point been rounded, then it can be assumed that the original value of an integer s follows an unknown distribution supported on the interval [s − 0.5, s + 0.5). For an integer data set of size N, this implies for an arbitrary integer j-th c-quantile q i , that the expected value for the quantile of the original, non-rounded data q r data equals the minimal value to be considered for q r plus the k-th order statistic for n values distributed according to the unknown distribution. Here, n is the number of values in the integer data set of equal value to q i , and k = ⌈(j · N)/c⌉ − u, where u denotes the number of integer data with smaller value than the quantile q i . Given n i. i. d. samples X 1 , . . . , X n , then their k-th order statistic is a random variable W (n,k) with probability density function ( ) n − 1 f W(n,k) (x) = n · · f X (x) · F X (x) k−1 · (1 − F X (x)) n−k (2.7) k − 1 Assuming X is distributed uniformly over the unit interval, then the k-th order statistic follows
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An Integrated Data Analysis Suite a
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Erklärung Hiermit erkläre ich, da
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Acknowledgment First of all I would
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Abstract The various parallel DNA s
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xii CONTENTS 2.6 A Parallelization
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2 CHAPTER 1. INTRODUCTION 1.2 Appro
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4 CHAPTER 1. INTRODUCTION genetic a
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Page 91 and 92: 4 Closing Remarks Routine analysis
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Page 96 and 97: 82 BIBLIOGRAPHY [9] S. Brenner, M.
Page 98 and 99: 84 BIBLIOGRAPHY [29] N. Cloonan, A.
Page 100 and 101: 86 BIBLIOGRAPHY [48] B. A. Methe, K
Page 102 and 103: 88 BIBLIOGRAPHY [72] S. Andrews. Fa
Page 104 and 105: 90 BIBLIOGRAPHY [98] M. A. DePristo
Page 106 and 107: 92 BIBLIOGRAPHY [124] W. J. Kent, C
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