Pattern discovery in bioinformatics: theory & algorithms
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, Fla. [u.a.]
Chapman & Hall/CRC
2008
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| Series: | Chapman & Hall/CRC mathematical and computational biology series
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Item Description: | hier auch unveränderte Nachdrucke |
| Physical Description: | 526 S. graph. Darst. 24cm |
| ISBN: | 9781584885498 9780367388898 1584885491 |
Staff View
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| adam_text | Contents
1 Introduction 1
1.1 Ubiquity of Patterns 1
1.2 Motivations from Biology 2
1.3 The Need for Rigor 2
1.4 Who is a Reader of this Book? 3
1.4.1 About this book 4
1 The Fundamentals 7
2 Basic Algorithmics 9
2.1 Introduction 9
2.2 Graphs 9
2.3 Tree Problem 1: Minimum Spanning Tree 14
2.3.1 Prim s algorithm 17
2.4 Tree Problem 2: Steiner Tree 21
2.5 Tree Problem 3: Minimum Mutation Labeling 22
2.5.1 Fitch s algorithm 23
2.6 Storing Retrieving Elements 27
2.7 Asymptotic Functions 30
2.8 Recurrence Equations 32
2.8.1 Counting binary trees 34
2.8.2 Enumerating unrooted trees (Prüfer sequence) ... 36
2.9 NP-Complete Class of Problems 40
2.10 Exercises 41
3 Basic Statistics 47
3.1 Introduction 47
3.2 Basic Probability 48
3.2.1 Probability space foundations 48
3.2.2 Multiple events (Bayes theorem) 50
3.2.3 Inclusion-exclusion principle 51
3.2.4 Discrete probability space 54
3.2.5 Algebra of random variables 57
3.2.6 Expectations 58
3.2.7 Discrete probability distribution (binomial, Poisson) 60
3.2.8 Continuous probability distribution (normal) .... 64
3.2.9 Continuous probability space (fi is R) 66
3.3 The Bare Truth about Inferential Statistics 69
3.3.1 Probability distribution invariants 70
3.3.2 Samples summary statistics 72
3.3.3 The central limit theorem 77
3.3.4 Statistical significance (p-value) 80
3.4 Summary 82
3.5 Exercises 82
4 What Are Patterns? 89
4.1 Introduction 89
4.2 Common Thread 90
4.3 Pattern Duality 90
4.3.1 Operators on p 92
4.4 Irredundant Patterns 92
4.4.1 Special case: maximality 93
4.4.2 Transitivity of redundancy 95
4.4.3 Uniqueness property 95
4.4.4 Case studies 96
4.5 Constrained Patterns 99
4.6 When is a Pattern Specification Nontrivial? 99
4.7 Classes of Patterns 100
4.8 Exercises 103
II Patterns on Linear Strings 111
5 Modeling the Stream of Life 113
5.1 Introduction 113
5.2 Modeling a Biopolymer 113
5.2.1 Repeats in DNA 114
5.2.2 Directionality of biopolymers 115
5.2.3 Modeling a random permutation 117
5.2.4 Modeling a random string 119
5.3 Bernoulli Scheine 120
5.4 Markov Chain 121
5.4.1 Stationary distribution 123
5.4.2 Computing probabilities 127
5.5 Hidden Markov Model (HMM) 128
5.5.1 The decoding problem (Viterbi algorithm) 130
5.6 Comparison of the Schemes 133
5.7 Conclusion 133
5.8 Exercises 134
6 String Pattern Specifications 139
6.1 Introduction 139
6.2 Notation 140
6.3 Solid Patterns 142
6.3.1 Maximality 144
6.3.2 Counting the maximal patterns 144
6.4 Rigid Patterns 149
6.4.1 Maximal rigid patterns 150
6.4.2 Enumerating maximal rigid patterns 152
6.4.3 Density-constrained patterns 156
6.4.4 Quorum-constrained patterns 157
6.4.5 Large-|S| input 158
6.4.6 Irredundant patterns 160
6.5 Extensible Patterns 164
6.5.1 Maximal extensible patterns 165
6.6 Generalizations 165
6.6.1 Homologous sets 165
6.6.2 Sequence on reals 167
6.7 Exercises 170
7 Algorithms Pattern Statistics 183
7.1 Introduction 183
7.2 Discovery Algorithm 183
7.3 Pattern Statistics 191
7.4 Rigid Patterns 191
7.5 Extensible Patterns 193
7.5.1 Nondegenerate extensible patterns 194
7.5.2 Degenerate extensible patterns 196
7.5.3 Correction factor for the dot character 197
7.6 Measure of Surprise 198
7.6.1 z-score 199
7.6.2 x-square ratio 199
7.6.3 Interplay of combinatorics statistics 200
7.7 Applications 201
7.8 Exercises 203
8 Motif Learning 213
8.1 Introduction: Local Multiple Alignment 213
8.2 Probabilistic Model: Motif Profile 214
8.3 The Learning Problem 215
8.4 Importance Measure 216
8.4.1 Statistical significance 216
8.4.2 Information content 219
8.5 Algorithms to Learn a Motif Profile 220
8.6 An Expectation Maximization Framework 222
8.6.1 The initial estimate po 222
8.6.2 Estimating z given p 223
8.6.3 Estimating p given z 224
8.7 A Gibbs Sampling Strategy 227
8.7.1 Estimating p given an alignment 227
8.7.2 Estimating background probabilities given Z . . . . 228
8.7.3 Estimating Z given p 228
8.8 Interpreting the Motif Profile in Terms of p 229
8.9 Exercises 230
9 The Subtle Motif 235
9.1 Introduction: Consensus Motif 235
9.2 Combinatorial Model: Subtle Motif 236
9.3 Distance between Motifs 238
9.4 Statistics of Subtle Motifs 240
9.5 Performance Score 245
9.6 Enumeration Schemes 246
9.6.1 Neighbor enumeration (exact) 246
9.6.2 Submotif enumeration (inexact) 249
9.7 A Combinatorial Algorithm 252
9.8 A Probabilistic Algorithm 255
9.9 A Modular Solution 257
9.10 Conclusion 259
9.11 Exercises 260
III Patterns on Meta-Data 263
10 Permutation Patterns 265
10.1 Introduction 265
10.1.1 Notation 266
10.2 How Many Permutation Patterns? 267
10.3 Maximality 268
10.3.1 P=1: Linear notation k PQ trees 269
10.3.2 P 1: Linear notation? 271
10.4 Parikh Mapping-based Algorithm 273
10.4.1 Tagging technique 275
10.4.2 Time complexity analysis 275
10.5 Intervals 278
10.5.1 The naive algorithm 280
10.5.2 The Uno-Yagiura RC algorithm 281
10.6 Intervals to PQ Trees 294
10.6.1 Irreducible intervals 295
10.6.2 Encoding intervals as a PQ tree 297
10.7 Applications 307
10.7.1 Case study I: Human and rat 308
10.7.2 Case study II: E. Coli K-12 and B. Subtilis 309
10.8 Conclusion 311
10.9 Exercises 312
11 Permutation Pattern Probabilities 323
11.1 Introduction 323
11.2 Unstructured Permutations 323
11.2.1 Multinomial coefficients 325
11.2.2 Patterns with multiplicities 328
11.3 Structured Permutations 329
11.3.1 P-arrangement 330
11.3.2 An incremental method 331
11.3.3 An upper bound on P-arrangements** 336
11.3.4 A lower bound on P-arrangements 341
11.3.5 Estimating the number of frontiers 342
11.3.6 Combinatorics to probabilities 345
11.4 Exercises 346
12 Topological Motifs 355
12.1 Introduction 355
12.1.1 Graph notation 355
12.2 What Are Topological Motifs? 356
12.2.1 Combinatorics in topologies 357
12.2.2 Input with self-isomorphisms 358
12.3 The Topological Motif 359
12.3.1 Maximality 367
12.4 Compact Topological Motifs 369
12.4.1 Occurrence-isomorphisms 369
12.4.2 Vertex indistinguishability 372
12.4.3 Compact list 373
12.4.4 Compact vertex, edge motif 373
12.4.5 Maximal compact lists 374
12.4.6 Conjugates of compact lists 374
12.4.7 Characteristics of compact lists 378
12.4.8 Maximal operations on compact lists 380
12.4.9 Maximal subsets of location lists 381
12.4.10 Binary relations on compact lists 384
12.4.11 Compact motifs from compact lists 384
12.5 The Discovery Method 392
12.5.1 The algorithm 393
12.6 Related Classical Problems 399
12.7 Applications 400
12.8 Conclusion 402
12.9 Exercises 402
13 Set-Theoretic Algorithmic Tools 417
13.1 Introduction 417
13.2 Some Basic Properties of Finite Sets 418
13.3 Partial Order Graph G( S,E) of Sets 419
13.3.1 Reduced partial order graph 420
13.3.2 Straddle graph 421
13.4 Boolean Closure of Sets 423
13.4.1 Intersection closure 423
13.4.2 Union closure 424
13.5 Consecutive (Linear) Arrangement of Set Members 426
13.5.1 PQ trees 426
13.5.2 Straddling sets 429
13.6 Maximal Set Intersection Problem (maxSIP) 434
13.6.1 Ordered enumeration trie 435
13.6.2 Depth first traversal of the trie 436
13.7 Minimal Set Intersection Problem (minSIP) 447
13.7.1 Algorithm 447
13.7.2 Minimal from maximal sets 448
13.8 Multi-Sets 450
13.8.1 Ordered enumeration trie of multi-sets 451
13.8.2 Enumeration algorithm 453
13.9 Adapting the Enumeration Scheine 455
13.10 Exercises 458
14 Expression Partial Order Motifs 469
14.1 Introduction 469
14.1.1 Motivation 470
14.2 Extracting (Monotone CNF) Boolean Expressions 471
14.2.1 Extracting biclusters 475
14.2.2 Extracting patterns in microarrays 478
14.3 Extracting Partial Orders 480
14.3.1 Partial Orders 480
14.3.2 Partial order construction problem 481
14.3.3 Excess in partial Orders 483
14.4 Statistics of Partial Orders 485
14.4.1 Computing Cex(B) 489
14.5 Redescriptions 493
14.6 Application: Partial Order of Expressions 494
14.7 Summary 495
14.8 Exercises 496
References 503
Index 515
|
| adam_txt |
Contents
1 Introduction 1
1.1 Ubiquity of Patterns 1
1.2 Motivations from Biology 2
1.3 The Need for Rigor 2
1.4 Who is a Reader of this Book? 3
1.4.1 About this book 4
1 The Fundamentals 7
2 Basic Algorithmics 9
2.1 Introduction 9
2.2 Graphs 9
2.3 Tree Problem 1: Minimum Spanning Tree 14
2.3.1 Prim's algorithm 17
2.4 Tree Problem 2: Steiner Tree 21
2.5 Tree Problem 3: Minimum Mutation Labeling 22
2.5.1 Fitch's algorithm 23
2.6 Storing Retrieving Elements 27
2.7 Asymptotic Functions 30
2.8 Recurrence Equations 32
2.8.1 Counting binary trees 34
2.8.2 Enumerating unrooted trees (Prüfer sequence) . 36
2.9 NP-Complete Class of Problems 40
2.10 Exercises 41
3 Basic Statistics 47
3.1 Introduction 47
3.2 Basic Probability 48
3.2.1 Probability space foundations 48
3.2.2 Multiple events (Bayes' theorem) 50
3.2.3 Inclusion-exclusion principle 51
3.2.4 Discrete probability space 54
3.2.5 Algebra of random variables 57
3.2.6 Expectations 58
3.2.7 Discrete probability distribution (binomial, Poisson) 60
3.2.8 Continuous probability distribution (normal) . 64
3.2.9 Continuous probability space (fi is R) 66
3.3 The Bare Truth about Inferential Statistics 69
3.3.1 Probability distribution invariants 70
3.3.2 Samples summary statistics 72
3.3.3 The central limit theorem 77
3.3.4 Statistical significance (p-value) 80
3.4 Summary 82
3.5 Exercises 82
4 What Are Patterns? 89
4.1 Introduction 89
4.2 Common Thread 90
4.3 Pattern Duality 90
4.3.1 Operators on p 92
4.4 Irredundant Patterns 92
4.4.1 Special case: maximality 93
4.4.2 Transitivity of redundancy 95
4.4.3 Uniqueness property 95
4.4.4 Case studies 96
4.5 Constrained Patterns 99
4.6 When is a Pattern Specification Nontrivial? 99
4.7 Classes of Patterns 100
4.8 Exercises 103
II Patterns on Linear Strings 111
5 Modeling the Stream of Life 113
5.1 Introduction 113
5.2 Modeling a Biopolymer 113
5.2.1 Repeats in DNA 114
5.2.2 Directionality of biopolymers 115
5.2.3 Modeling a random permutation 117
5.2.4 Modeling a random string 119
5.3 Bernoulli Scheine 120
5.4 Markov Chain 121
5.4.1 Stationary distribution 123
5.4.2 Computing probabilities 127
5.5 Hidden Markov Model (HMM) 128
5.5.1 The decoding problem (Viterbi algorithm) 130
5.6 Comparison of the Schemes 133
5.7 Conclusion 133
5.8 Exercises 134
6 String Pattern Specifications 139
6.1 Introduction 139
6.2 Notation 140
6.3 Solid Patterns 142
6.3.1 Maximality 144
6.3.2 Counting the maximal patterns 144
6.4 Rigid Patterns 149
6.4.1 Maximal rigid patterns 150
6.4.2 Enumerating maximal rigid patterns 152
6.4.3 Density-constrained patterns 156
6.4.4 Quorum-constrained patterns 157
6.4.5 Large-|S| input 158
6.4.6 Irredundant patterns 160
6.5 Extensible Patterns 164
6.5.1 Maximal extensible patterns 165
6.6 Generalizations 165
6.6.1 Homologous sets 165
6.6.2 Sequence on reals 167
6.7 Exercises 170
7 Algorithms Pattern Statistics 183
7.1 Introduction 183
7.2 Discovery Algorithm 183
7.3 Pattern Statistics 191
7.4 Rigid Patterns 191
7.5 Extensible Patterns 193
7.5.1 Nondegenerate extensible patterns 194
7.5.2 Degenerate extensible patterns 196
7.5.3 Correction factor for the dot character 197
7.6 Measure of Surprise 198
7.6.1 z-score 199
7.6.2 x-square ratio 199
7.6.3 Interplay of combinatorics statistics 200
7.7 Applications 201
7.8 Exercises 203
8 Motif Learning 213
8.1 Introduction: Local Multiple Alignment 213
8.2 Probabilistic Model: Motif Profile 214
8.3 The Learning Problem 215
8.4 Importance Measure 216
8.4.1 Statistical significance 216
8.4.2 Information content 219
8.5 Algorithms to Learn a Motif Profile 220
8.6 An Expectation Maximization Framework 222
8.6.1 The initial estimate po 222
8.6.2 Estimating z given p 223
8.6.3 Estimating p given z 224
8.7 A Gibbs Sampling Strategy 227
8.7.1 Estimating p given an alignment 227
8.7.2 Estimating background probabilities given Z . . . . 228
8.7.3 Estimating Z given p 228
8.8 Interpreting the Motif Profile in Terms of p 229
8.9 Exercises 230
9 The Subtle Motif 235
9.1 Introduction: Consensus Motif 235
9.2 Combinatorial Model: Subtle Motif 236
9.3 Distance between Motifs 238
9.4 Statistics of Subtle Motifs 240
9.5 Performance Score 245
9.6 Enumeration Schemes 246
9.6.1 Neighbor enumeration (exact) 246
9.6.2 Submotif enumeration (inexact) 249
9.7 A Combinatorial Algorithm 252
9.8 A Probabilistic Algorithm 255
9.9 A Modular Solution 257
9.10 Conclusion 259
9.11 Exercises 260
III Patterns on Meta-Data 263
10 Permutation Patterns 265
10.1 Introduction 265
10.1.1 Notation 266
10.2 How Many Permutation Patterns? 267
10.3 Maximality 268
10.3.1 P=1: Linear notation k PQ trees 269
10.3.2 P 1: Linear notation? 271
10.4 Parikh Mapping-based Algorithm 273
10.4.1 Tagging technique 275
10.4.2 Time complexity analysis 275
10.5 Intervals 278
10.5.1 The naive algorithm 280
10.5.2 The Uno-Yagiura RC algorithm 281
10.6 Intervals to PQ Trees 294
10.6.1 Irreducible intervals 295
10.6.2 Encoding intervals as a PQ tree 297
10.7 Applications 307
10.7.1 Case study I: Human and rat 308
10.7.2 Case study II: E. Coli K-12 and B. Subtilis 309
10.8 Conclusion 311
10.9 Exercises 312
11 Permutation Pattern Probabilities 323
11.1 Introduction 323
11.2 Unstructured Permutations 323
11.2.1 Multinomial coefficients 325
11.2.2 Patterns with multiplicities 328
11.3 Structured Permutations 329
11.3.1 P-arrangement 330
11.3.2 An incremental method 331
11.3.3 An upper bound on P-arrangements** 336
11.3.4 A lower bound on P-arrangements 341
11.3.5 Estimating the number of frontiers 342
11.3.6 Combinatorics to probabilities 345
11.4 Exercises 346
12 Topological Motifs 355
12.1 Introduction 355
12.1.1 Graph notation 355
12.2 What Are Topological Motifs? 356
12.2.1 Combinatorics in topologies 357
12.2.2 Input with self-isomorphisms 358
12.3 The Topological Motif 359
12.3.1 Maximality 367
12.4 Compact Topological Motifs 369
12.4.1 Occurrence-isomorphisms 369
12.4.2 Vertex indistinguishability 372
12.4.3 Compact list 373
12.4.4 Compact vertex, edge motif 373
12.4.5 Maximal compact lists 374
12.4.6 Conjugates of compact lists 374
12.4.7 Characteristics of compact lists 378
12.4.8 Maximal operations on compact lists 380
12.4.9 Maximal subsets of location lists 381
12.4.10 Binary relations on compact lists 384
12.4.11 Compact motifs from compact lists 384
12.5 The Discovery Method 392
12.5.1 The algorithm 393
12.6 Related Classical Problems 399
12.7 Applications 400
12.8 Conclusion 402
12.9 Exercises 402
13 Set-Theoretic Algorithmic Tools 417
13.1 Introduction 417
13.2 Some Basic Properties of Finite Sets 418
13.3 Partial Order Graph G( S,E) of Sets 419
13.3.1 Reduced partial order graph 420
13.3.2 Straddle graph 421
13.4 Boolean Closure of Sets 423
13.4.1 Intersection closure 423
13.4.2 Union closure 424
13.5 Consecutive (Linear) Arrangement of Set Members 426
13.5.1 PQ trees 426
13.5.2 Straddling sets 429
13.6 Maximal Set Intersection Problem (maxSIP) 434
13.6.1 Ordered enumeration trie 435
13.6.2 Depth first traversal of the trie 436
13.7 Minimal Set Intersection Problem (minSIP) 447
13.7.1 Algorithm 447
13.7.2 Minimal from maximal sets 448
13.8 Multi-Sets 450
13.8.1 Ordered enumeration trie of multi-sets 451
13.8.2 Enumeration algorithm 453
13.9 Adapting the Enumeration Scheine 455
13.10 Exercises 458
14 Expression Partial Order Motifs 469
14.1 Introduction 469
14.1.1 Motivation 470
14.2 Extracting (Monotone CNF) Boolean Expressions 471
14.2.1 Extracting biclusters 475
14.2.2 Extracting patterns in microarrays 478
14.3 Extracting Partial Orders 480
14.3.1 Partial Orders 480
14.3.2 Partial order construction problem 481
14.3.3 Excess in partial Orders 483
14.4 Statistics of Partial Orders 485
14.4.1 Computing Cex(B) 489
14.5 Redescriptions 493
14.6 Application: Partial Order of Expressions 494
14.7 Summary 495
14.8 Exercises 496
References 503
Index 515 |
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| any_adam_object_boolean | 1 |
| author | Parida, Laxmi |
| author_facet | Parida, Laxmi |
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| callnumber-subject | QH - Natural History and Biology |
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| ctrlnum | (OCoLC)123053354 (DE-599)BSZ263228940 |
| dewey-full | 572.80285 570.28564 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 572 - Biochemistry 570 - Biology |
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| dewey-search | 572.80285 570.28564 |
| dewey-sort | 3572.80285 |
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| discipline | Biologie Informatik |
| discipline_str_mv | Biologie Informatik |
| format | Book |
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| id | DE-604.BV023354544 |
| illustrated | Illustrated |
| index_date | 2024-07-02T21:06:29Z |
| indexdate | 2024-07-09T21:16:41Z |
| institution | BVB |
| isbn | 9781584885498 9780367388898 1584885491 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016538104 |
| oclc_num | 123053354 |
| open_access_boolean | |
| owner | DE-M49 DE-BY-TUM DE-188 DE-83 DE-1043 |
| owner_facet | DE-M49 DE-BY-TUM DE-188 DE-83 DE-1043 |
| physical | 526 S. graph. Darst. 24cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Chapman & Hall/CRC |
| record_format | marc |
| series2 | Chapman & Hall/CRC mathematical and computational biology series |
| spelling | Parida, Laxmi Verfasser aut Pattern discovery in bioinformatics theory & algorithms Laxmi Parida Boca Raton, Fla. [u.a.] Chapman & Hall/CRC 2008 526 S. graph. Darst. 24cm txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC mathematical and computational biology series hier auch unveränderte Nachdrucke Bioinformatics Pattern recognition systems Computational biology Bioinformatik (DE-588)4611085-9 gnd rswk-swf Mustererkennung (DE-588)4040936-3 gnd rswk-swf Bioinformatik (DE-588)4611085-9 s Mustererkennung (DE-588)4040936-3 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016538104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Parida, Laxmi Pattern discovery in bioinformatics theory & algorithms Bioinformatics Pattern recognition systems Computational biology Bioinformatik (DE-588)4611085-9 gnd Mustererkennung (DE-588)4040936-3 gnd |
| subject_GND | (DE-588)4611085-9 (DE-588)4040936-3 |
| title | Pattern discovery in bioinformatics theory & algorithms |
| title_auth | Pattern discovery in bioinformatics theory & algorithms |
| title_exact_search | Pattern discovery in bioinformatics theory & algorithms |
| title_exact_search_txtP | Pattern discovery in bioinformatics theory & algorithms |
| title_full | Pattern discovery in bioinformatics theory & algorithms Laxmi Parida |
| title_fullStr | Pattern discovery in bioinformatics theory & algorithms Laxmi Parida |
| title_full_unstemmed | Pattern discovery in bioinformatics theory & algorithms Laxmi Parida |
| title_short | Pattern discovery in bioinformatics |
| title_sort | pattern discovery in bioinformatics theory algorithms |
| title_sub | theory & algorithms |
| topic | Bioinformatics Pattern recognition systems Computational biology Bioinformatik (DE-588)4611085-9 gnd Mustererkennung (DE-588)4040936-3 gnd |
| topic_facet | Bioinformatics Pattern recognition systems Computational biology Bioinformatik Mustererkennung |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016538104&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT paridalaxmi patterndiscoveryinbioinformaticstheoryalgorithms |