Bioinformatics Algorithms: Techniques and Applications

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DISCUSSION 367 TABLE 16.1 Phasing Accuracy of HIT Measured by the Switch Distancea Dataset HIT5 HIT6 HIT7 HIT8 HIT9 HIT10 HIT11 HIT∗ CEU-100 0.21 0.21 0.21 0.22 0.21 0.21 0.21 0.21 YRI-100 0.29 0.28 0.28 0.28 0.28 0.29 0.29 0.28 CEU-200 0.078 0.076 0.073 0.072 0.072 0.071 0.071 0.072 YRI-200 0.13 0.12 0.12 0.11 0.11 0.11 0.11 0.11 CEU-1000 0.042 0.038 0.037 0.036 0.035 0.035 0.035 0.035 YRI-1000 0.076 0.069 0.063 0.060 0.057 0.055 0.055 0.057 Pop1 0.21 0.23 0.24 0.19 0.22 0.21 0.23 0.21 Pop2 0.17 0.17 0.17 0.17 0.17 0.16 0.16 0.18 Pop3 0.20 0.21 0.17 0.20 0.21 0.20 0.17 0.19 Daly et al. 0.029 0.028 0.034 0.030 0.031 0.034 0.034 0.030 a For CEU-200, YRI-200, CEU-1000, and YRI-1000 the switch distance is averaged over the 22 included datasets. TABLE 16.2 Phasing Accuracy of Some Methods Measured by the Switch Distance a Dataset HIT ∗ fastPHASE GERBIL PHASE HAP CEU-100 0.21 0.20 0.22 0.20 — YRI-100 0.28 0.27 0.30 0.26 — CEU-200 0.072 0.068 0.085 — — YRI-200 0.11 0.11 0.14 — — CEU-1000 0.035 0.033 — — — YRI-1000 0.057 0.051 — — — Pop1 0.21 0.21 0.25 0.21 0.26 Pop2 0.18 0.16 0.19 0.15 0.18 Pop3 0.19 0.19 0.21 0.17 0.19 Daly et al. 0.030 0.027 0.031 0.037 0.039 a For CEU-200, YRI-200, CEU-1000, and YRI-1000 the switch distance is averaged over the 22 included datasets. that the performance differences of the methods are consistent across different datasets:GERBIL is seldom more accurate than HIT*, and HIT*, in turn, is just occasionally more accurate than fastPHASE. Figure 16.3 also shows a comparison of HIT* against PHASE on the 100-SNP datasets. On the CEU-100 datasets HIT* is consistently slightly behind PHASE. Interestingly, on the YRI-100 datasets HIT* is more accurate than PHASE on the hard cases, whereas PHASE is more accurate on the easier cases. 16.6 DISCUSSION We have described a hidden Markov model for SNP haplotypes. In the HMM each haplotype in the present generation is viewed as a mosaic of a limited number of common “founder” haplotypes. The founder haplotypes should be understood as a sort of minimal haplotype “basis” or “effective ancestral material” rather than any
368 PHASING GENOTYPES USING A HIDDEN MARKOV MODEL fastPHASE GERBIL fastPHASE 0.2 0.15 0.1 0.05 CEU−200 0 0 0.05 0.1 HIT* 0.15 0.2 0.2 0.15 0.1 0.05 0.08 0.07 0.06 0.05 0.04 0.03 0.02 0.01 CEU−200 0 0 0.05 0.1 HIT* 0.15 0.2 CEU−1000 0 0 0.02 0.04 HIT* 0.06 0.08 fastPHASE GERBIL fastPHASE 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 YRI−200 0 0 0.1 0.2 HIT* 0.3 0.4 0.4 0.35 0.3 0.25 0.2 0.15 0.1 0.05 0 0 0.1 0.2 HIT* 0.3 0.4 0.2 0.15 0.1 0.05 YRI−200 YRI−1000 0 0 0.05 0.1 HIT* 0.15 0.2 FIGURE 16.2 Comparison of phasing accuracy on 200-SNP and 1000-SNP HapMap datasets. For each dataset (from chromosomes 1, 2, ..., 22) and method (HIT*, fastPHASE, and GERBIL) the switch distance between the true and the reconstructed haplotype pairs is shown.
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BIOINFORMATICS ALGORITHMS
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Copyright © 2008 by John Wiley & S
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vi CONTENTS 6 A Survey of Seeding f
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PREFACE Bioinformatics, broadly def
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CONTRIBUTORS Sudha Balla, Departmen
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CONTRIBUTORS xiii Steven Hecht Orza
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1 EDUCATING BIOLOGISTS IN THE 21ST
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EDUCATING BIOLOGISTS IN THE 21ST CE
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EDUCATING BIOLOGISTS IN THE 21ST CE
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2 DYNAMIC PROGRAMMING ALGORITHMS FO
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SEQUENCE ALIGNMENT: GLOBAL, LOCAL,
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ecurrence: SEQUENCE ALIGNMENT: GLOB
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DYNAMIC PROGRAMMING ALGORITHMFOR RN
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DYNAMIC PROGRAMMING ALGORITHMFOR RN
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DYNAMIC PROGRAMMING ALGORITHMS FOR
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REFERENCES 25 the flexible structur
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REFERENCES 27 32. Gusfield D. Effic
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3 GRAPH THEORETICAL APPROACHES TO D
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GRAPH THEORY BACKGROUND 31 beginnin
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GRAPH THEORY BACKGROUND 33 FIGURE 3
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GRAPH THEORY BACKGROUND 35 chordal
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GRAPH THEORY BACKGROUND 37 decompos
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RECONSTRUCTING PHYLOGENIES 39 are (
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RECONSTRUCTING PHYLOGENIES 41 only
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FORMATION OF MULTIPROTEIN COMPLEXES
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3.4.1 Ribosomal Assembly FORMATION
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ACKNOWLEDGMENTS REFERENCES 51 This
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REFERENCES 53 37. Golumbic MC, Hart
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4 ADVANCES IN HIDDEN MARKOV MODELS
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HIDDEN MARKOV MODELS FOR SEQUENCE A
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ALTERNATIVES TO VITERBI DECODING 63
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Noncoding Coding Intron (a) Without
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also have this same label). We get
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change as follows: GENERALIZED HIDD
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0.00004 0.00002 0.00000 0 20000 400
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HMMS WITH MULTIPLE OUTPUTS OR EXTER
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TRAINING THE PARAMETERS OF AN HMM 8
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CONCLUSION 85 of parameters compare
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REFERENCES 87 4. Altun Y, Tsochanta
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REFERENCES 89 42. Krogh A. Using da
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REFERENCES 91 77. Xu EW, Kearney P,
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94 SORTING- AND FFT-BASED TECHNIQUE
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100 SORTING- AND FFT-BASED TECHNIQU
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6 A SURVEY OF SEEDING FOR SEQUENCE
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ALIGNMENTS 119 6.2.1 Formal Definit
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TRADITIONAL APPROACHES TO HEURISTIC
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MORE CONTEMPORARY SEEDING APPROACHE
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MORE COMPLICATED SEED DESCRIPTIONS
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SOME THEORETICAL ISSUES IN ALIGNMEN
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REFERENCES 141 6. Brown DG. Optimiz
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7 THE COMPARISON OF PHYLOGENETIC NE
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INTRODUCTION 145 known phylogeny re
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BASIC DEFINITIONS 147 The undirecte
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BASIC DEFINITIONS 149 N1 displays N
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A B C A B C SUBTREES AND SUBNETWORK
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SUBTREES AND SUBNETWORKS 153 of x a
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SUBTREES AND SUBNETWORKS 155 1. it
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SUPERTREES AND SUPERNETWORKS 157 By
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SUPERTREES AND SUPERNETWORKS 159 Go
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SUPERTREES AND SUPERNETWORKS 161 Th
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RECONCILIATION OF GENE TREES AND SP
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REFERENCES 173 21. Gòrecki P, Tiur
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8 FORMAL MODELS OF GENE CLUSTERS An
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8.2 GENOME PLASTICITY 8.2.1 Genome
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GENOME PLASTICITY 181 FIGURE 8.2 An
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BASIC CONCEPTS 183 “more or less
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BASIC CONCEPTS 185 of {m, o, s}. On
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MODELS OF GENE CLUSTERS 187 Definit
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4, 2, 3, 1, 11, 10, 9, 8, 7, 6, 5 4
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MODELS OF GENE CLUSTERS 191 FIGURE
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MODELS OF GENE CLUSTERS 193 another
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MODELS OF GENE CLUSTERS 195 of gene
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MODELS OF GENE CLUSTERS 197 The two
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REFERENCES 199 flexibility by bound
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REFERENCES 201 28. Hoberman R, Dura
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9 INTEGER LINEAR PROGRAMMING TECHNI
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BASIC PROBLEM SPECIFICATION 205 a n
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INTEGER LINEAR PROGRAMMING FORMULAT
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INTEGER LINEAR PROGRAMMING FORMULAT
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9.4 EXTENSIONS AND VARIATIONS EXTEN
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i=1 EXTENSIONS AND VARIATIONS 213 H
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9.5 COMPUTATIONAL RESULTS COMPUTATI
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DISCUSSION 217 TABLE 9.2 Cluster Si
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DISCUSSION 219 FIGURE 9.5 Manually
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ACKNOWLEDGMENTS REFERENCES 221 We t
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224 EFFICIENT COMBINATORIAL ALGORIT
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11 ALGORITHMS FOR MULTIPLEX PCR PRI
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INTRODUCTION 243 problem: given a s
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1. p hybridizes at position t of f
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Thus, constraints 11.7 can be repla
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A GREEDY ALGORITHM 249 FIGURE 11.3
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EXPERIMENTAL RESULTS 251 11.5.1 Amp
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#primers/(2x#SNPs) (%) #primers/(2x
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TABLE 11.2 (Continued ) EXPERIMENTA
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REFERENCES 257 p, discard all candi
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12 RECENT DEVELOPMENTS IN ALIGNMENT
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12.2 MULTIPLE SEQUENCE ALIGNMENT 12
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MULTIPLE SEQUENCE ALIGNMENT 263 The
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MOTIF FINDING 265 Marsan and Sagot
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BIOLOGICAL NETWORK ANALYSIS 267 mul
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DISCUSSION 269 an interaction pair
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REFERENCES 271 13. Bucka-Lassen K,
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REFERENCES 273 52. Lee C, Grasso C,
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REFERENCES 275 90. Stormo GD, Hartz
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PART III MICROARRAY DESIGN AND DATA
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280 ALGORITHMS FOR OLIGONUCLEOTIDE
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14 CLASSIFICATION ACCURACY BASED MI
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INTRODUCTION 305 Decomposition (SVD
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METHODS 307 Note that in most of th
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estimated as K� 1 ai,j = aik,j. d
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METHODS 311 [7]. The KNN-classifier
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ROWimpute-KNN ROWimpute-SVM KNNimpu
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Page 328 and 329: REFERENCES 325 From these two plots
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Page 332 and 333: 330 META-ANALYSIS OF MICROARRAY DAT
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Page 390 and 391: DISCUSSION 389 2SNP also produced r
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Page 396 and 397: 18 OPTIMIZATION METHODS FOR GENOTYP
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Page 408 and 409: RESULTS AND DISCUSSION 407 to decid
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Page 414 and 415: RESULTS AND DISCUSSION 413 nonindex
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19 TOPOLOGICAL INDICES IN COMBINATO
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TOPOLOGICAL INDICES 421 The quantit
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Theorem 19.2 Let T = (V, E) be a tr
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HOSOYA POLYNOMIAL 425 The Laplacian
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H2(G, x) = � {u,v}⊆V INVERSE WI
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HEXAGONAL SYSTEMS 429 hexagonal sys
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C 2 HEXAGONAL SYSTEMS 431 FIGURE 19
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THE WIENER INDEX OF PEPTOIDS 433 Th
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if R ≥ L, then π(Lp) = i; Lp = L
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REFERENCES 437 19. Entringer RC, Me
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20 EFFICIENT ALGORITHMS FOR STRUCTU
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COMPOUND REPRESENTATION 441 FIGURE
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COMPOUND REPRESENTATION 443 breakag
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TABLE 20.1 Bond List of Aspirin Bon
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COMPOUND REPRESENTATION 447 20.2.5
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Initial class value for node A A 3
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CHEMICAL COMPOUND DATABASE 451 In c
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CHEMICAL COMPOUND DATABASE 453 taki
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CHEMICAL COMPOUND DATABASE 455 Othe
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REFERENCES 457 lab may take months
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REFERENCES 459 22. Curco D, Rodrigu
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REFERENCES 461 61. An J, Nakama T,
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REFERENCES 463 101. Shen J. HAD An
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466 COMPUTATIONAL APPROACHES TO PRE
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INDEX 2SNP computer program 383, 38
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degeneracy 101-104, 112 degenerate
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lowest p-value method 484-486 max-g
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pseudoknots 20 p-value 339-343, 347
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