Bioinformatics Algorithms: Techniques and Applications

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RESULTS 387 TABLE 17.6 The Distribution of Indirect Estimates of Haplotype Numbers for Cases 1–5 (Number of Sample Paths). For Each Case, the Lower and Upper Bounds of AB Haplotypes are the Lowest and the Highest Possible Number, Respectively. Indirect Estimates Generated by RB are Identical to the Direct Estimates Shown in Table 17.4. Bold Numbers Denote P < 0.05; Each P Value is the Result of an Exact Test Comparing the Distributions of Outcomes from the two Simulations (see text for the Exact Value) Method EM PL-EM Haplotyper Phase MS ENT Number of AB Simulation Case Haplotypes 1 2 1 2 1 2 1 2 1 2 27 4917 5044 4458 4739 5065 4832 904 894 4958 5050 1 28 0 1 0 0 0 0 176 173 0 0 29 5083 4955 5542 5261 4935 5168 920 933 5042 4950 84 7197 7312 7180 7528 7729 7783 1663 1638 6785 6829 2 85 –162 0 0 0 0 0 0 12 17 0 0 163 2803 2688 2820 2472 2271 2217 325 345 3215 3171 47 4793 4893 5002 5139 4432 4599 459 427 5235 5139 3 48 –187 0 0 0 0 0 0 101 92 0 0 188 5207 5107 4998 4861 5568 5401 1440 1481 4765 4861 55 0 0 0 0 1666 1846 0 0 1370 1398 4 56–67 0 0 0 0 0 0 0 0 0 0 68 10000 10000 10000 10000 8334 8154 2000 2000 8630 8602 21 4906 5025 5276 4783 4333 4501 455 438 4552 4514 5 22 –102 0 0 0 0 0 0 29 38 0 0 103 5094 4975 4724 5217 5667 5499 1516 1524 5448 5486 The direct estimates generated by HaploFreq are shown in Table 17.5. HaploFreq found one of the global maxima for case 1. It found the local maximum for cases 3 and 5 and the global maximum for cases 2 and 4. 17.3.2 Indirect Estimates The indirect estimates shown in Table 17.6 were generally quite different from direct estimates. The reason is that in any given sample path of the EM-based methods, all individuals with an ambiguous genotype are assigned the same most probable haplotype pair. However, the identity of this pair may differ across sample paths if there is more than one maximum on the likelihood surface. The result is the binary outcome of indirect frequency estimates observed for the cases that have two maxima (1, 2, 3, and 5). In contrast, case 4 has a single outcome because there is only one maximum. The EM algorithm produced distributions of indirect estimates that were not significantly different (case 1: p = 0.072; case 2: p = 0.071; case 3: p = 0.161; case 5: p = 0.095).
388 ANALYTICAL AND ALGORITHMIC METHODS The PL–EM algorithm produced indirect estimates that were generally similar to those produced by our EM algorithm. However, for three of five cases, the distributions produced by the two simulations were significantly different (case 1: p
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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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Classification accuracies of SRBCT
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Classification accuracies of SRBCT
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REFERENCES 325 From these two plots
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REFERENCES 327 18. Troyanskaya OG,
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330 META-ANALYSIS OF MICROARRAY DAT
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Page 338 and 339: 336 META-ANALYSIS OF MICROARRAY DAT
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Page 368 and 369: DISCUSSION 367 TABLE 16.1 Phasing A
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Page 392 and 393: ACKNOWLEDGMENTS 391 haplotypes need
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Page 396 and 397: 18 OPTIMIZATION METHODS FOR GENOTYP
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Page 402 and 403: DISEASE ASSOCIATION SEARCH 401 18.2
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Page 408 and 409: RESULTS AND DISCUSSION 407 to decid
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Page 412 and 413: RESULTS AND DISCUSSION 411 TABLE 18
Page 414 and 415: RESULTS AND DISCUSSION 413 nonindex
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Page 424 and 425: HOSOYA POLYNOMIAL 425 The Laplacian
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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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