Applications of fuzzy logic in bioinformatics

A man disappears. The woman who loves him is left scarred and haunted. In her fierce, one-of-a-kind debut, Rebecca Lindenberg tells the storyÂin verseÂof her passionate relationship with Craig Arnold, a much-respected poet who disappeared in 2009 while hiking a volcano in Japan. Lindenberg's billowing, I-contain-multitudes style lays bare the poet's sadnesses, joys, and longings in poems that are lyric and narrative, at once plainspoken and musically elaborate.

Regarding her role in Arnold's story, Lindenberg writes with clear-eyed humility and endearing dignity: ÂThe girl with the ink-stained teeth / knows she's famous / in a tiny, tragic way. / She's not / daft, after all." And then later, playfully, of her travels in Italy with the poet, her lover: ÂThe carabinieri / wanted to know if there were bears / in our part of America. Yes, we said, / many bears. Man-eating bears? Yes, of course, / many man-eating bears." Every poem in this collection bursts with humor, pathos, verveÂand an utterly unique, soulful voice.

This widely anticipated debut, already selected as a finalist for several prominent book awards, marks the first collection in the newly minted McSweeney's Poetry Series. MPS is an imprint which seeks to publish a broad range of excellent new poetry collections in exquisitely designed hardcoversÂpoetry that's useful and meaningful to anyone in any walk of life.

Foreword	p. vii
Preface	p. xi
1 Introduction to Bioinformatics	p. 1
1.1 What Is Bioinformatics	p. 1
1.2 A Brief History of Bioinformatics	p. 2
1.3 Scope of Bioinformatics	p. 8
1.4 Major Challenges in Bioinformatics	p. 13
1.5 Bioinformatics and Computer Science	p. 14
2 Introduction to Fuzzy Set Theory and Fuzzy Logic	p. 16
2.1 Where Does Fuzzy Logic Fit in Computational Science?	p. 16
2.2 Why Do We Need to Use Fuzziness in Biology?	p. 17
2.3 Brief History of the Field	p. 21
2.4 Fuzzy Membership Functions and Operators	p. 23
2.4.1 Membership functions	p. 23
2.4.2 Basic fuzzy set operators	p. 27
2.4.3 Compensatory operators	p. 33
2.5 Fuzzy Relations and Fuzzy Logic Inference	p. 37
2.6 Fuzzy Clustering	p. 48
2.6.1 Fuzzy C-Means	p. 49
2.6.2 Extension to fuzzy C-Means	p. 54
2.6.3 Possibilistic C-Means (PCM)	p. 59
2.7 Fuzzy K-Nearest Neighbors	p. 63
2.8 Fuzzy Measures and Fuzzy Integrals	p. 66
2.8.1 Fuzzy measures	p. 67
2.8.2 Fuzzy integrals	p. 69
2.9 Summary and Final Thoughts	p. 72
3 Fuzzy Similarities in Ontologies	p. 73
3.1 Introduction	p. 73
3.2 Definition of Ontology-Based Similarity	p. 76
3.3 Set-Based Similarity Measure	p. 80
3.3.1 Pair-wise aggregation	p. 80
3.3.2 Bag of words similarities	p. 84
3.4 Fuzzy Measure Similarity	p. 85
3.5 Fuzzy Measure Similarity for Augmented Sets of Ontology Objects	p. 86
3.6 Choquet Fuzzy Integral Similarity Measure	p. 87
3.7 Examples and Applications of Fuzzy Measure Similarity Using GO Terms	p. 90
3.7.1 Lymphoma case study	p. 90
3.7.2 Gene clustering using Gene Ontology annotations	p. 92
3.7.3 Gene summarization using Gene Ontology terms	p. 98
3.8 Ontology Similarity in Data Mining	p. 99
3.9 Discussion and Summary	p. 102
4 Fuzzy Logic in Structural Bioinformatics	p. 103
4.1 Introduction	p. 103
4.2 Protein Secondary Structure Prediction	p. 106
4.3 Protein Solvent Accessibility Prediction	p. 116
4.4 Protein Structure Matching Using Fuzzy Alignments	p. 118
4.5 Protein Similarity Calculation Using Fuzzy Contact Maps	p. 124
4.6 Protein Structure Class Classification	p. 126
4.7 Summary	p. 130
5 Application of Fuzzy Logic in Microarray Data Analyses	p. 131
5.1 Introduction	p. 131
5.1.1 Microarray data description	p. 134
5.1.2 Microarray processing algorithms for gene selection and patient classification	p. 136
5.1.3 Microarray processing algorithms for gene regulatory network discovery	p. 137
5.2 Clustering Algorithms	p. 138
5.2.1 (Dis)similarity measures for microarray data	p. 140
5.2.2 Fuzzy C-means (FCM)	p. 144
5.2.3 Relational fuzzy C-means	p. 148
5.2.4 Fuzzy co-clustering algorithms	p. 152
5.3 Inferring Gene Networks Using Fuzzy Rule Systems	p. 155
5.4 Discussion and Summary	p. 159
6 Other Applications	p. 160
6.1 Overview	p. 160
6.2 Applications in Biological Sequence Analyses	p. 161
6.2.1 Protein sequence comparison	p. 161
6.2.2 Application in sequence family classification	p. 164
6.2.3 Application in motif identification	p. 165
6.2.4 Application in protein subcellular localization prediction	p. 166
6.2.5 Genomic structure prediction	p. 167
6.3 Application in Computational Proteomics	p. 168
6.3.1 Electrophoresis analysis	p. 169
6.3.2 Protein identification through mass-spec	p. 170
6.4 Application in Drug Design	p. 171
6.5 Discussion and Summary	p. 174
7 Summary and Outlook	p. 176
Appendix I Fundamental Biological Concepts	p. 179
AI.1 DNA, RNA and Genome	p. 179
AI.1.1 DNA (deoxyribonucleic acid)	p. 179
AI.1.2 RNA (ribonucleic acid)	p. 181
AI.1.3 Genome	p. 181
AI.2 Protein and Its Structure	p. 182
AI.3 Central Dogma of Biology	p. 186
Appendix II Online Resources	p. 189
AII.1 Online Resources for Molecular Biology	p. 189
AII.2 Online Resources for Bioinformatics	p. 190
AII.2.1 Protein structure	p. 191
AII.2.1.1 Protein structure database	p. 191
AII.2.1.2 Protein structure visualization	p. 191
AII.2.2 Microarray	p. 192
AII.2.2.1 Microarray databases	p. 192
AII.2.2.2 Microarray analysis tool	p. 193
AII.2.3 Gene ontology	p. 194
AII.2.4 Online portals for bioinformatics	p. 194
AII.3 Online Resources for Fuzzy Set Theory and Fuzzy Logic	p. 195
Bibliography	p. 196
Index	p. 222

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