Pattern Discovery in Bioinformatics: Theory and Algorithms

 INTRODUCTION
Ubiquity of Patterns
Motivations Form Biology
The Need for Rigor
Who Is a Reader of This Book?


THE FUNDAMENTALS
BASIC ALGORITHMICS
Introduction
Graphs
Tree Problem 1: (Minimum Spanning Tree)
Tree Problem 2: (Steiner Tree)
Tree Problem 3: (Minimum Mutation Labeling)
Storing and Retrieving Elements
Asymptotic Functions
Recurrence Equations
NP-Complete Class of Problems

BASIC STATISTICS
Introduction
Basic Probability
The Bare Truth about Inferential Statistics
Summary

WHAT ARE PATTERNS?
Introduction
Common Thread
Pattern Duality
Irredundant Patterns
Constrained Patterns
When Is a Pattern Specification Non-Trivial?
Classes of Patterns


PATTERNS ON LINEAR STRINGS
MODELING THE STREAM OF LIFE
Introduction
Modeling a Biopolymer
Bernoulli Scheme
Markov Chain
Hidden Markov Model (HMM)
Comparison of the Schemes
Conclusion

STRING PATTERN SPECIFICATIONS
Introduction
Notation
Solid Patterns
Rigid Patterns
Extensible Patterns
Generalizations

ALGORITHMS AND PATTERN STATISTICS
Introduction
Discovery Algorithm
Pattern Statistics
Rigid Patterns
Extensible Patterns
Measure of Surprise
Applications

MOTIF LEARNING
Introduction: Local Multiple Alignment
Probabilistic Model: Motif Profile
The Learning Problem
Importance Measure
Algorithms to Learn a Motif Profile
An Expectation Maximization Framework
A Gibbs Sampling Strategy
Interpreting the Motif Profile in Terms of p

THE SUBTLE MOTIF
Introduction: Consensus Motif
Combinatorial Model: Subtle Motif
Distance between Motifs
Statistics of Subtle Motifs
Performance Score
Enumeration Schemes
A Combinatorial Algorithm
A Probabilistic Algorithm
A Modular Solution
Conclusion


PATTERNS ON META-DATA
PERMUTATION PATTERNS
Introduction
Notation
How Many Permutation Patterns?
Maximality
Parikh Mapping-Based Algorithm
Intervals
Intervals to PQ Trees
Applications
Conclusion

PERMUTATION PATTERN PROBABILITIES
Introduction
Unstructured Permutations
Structured Permutations

TOPOLOGICAL MOTIFS
Introduction
What Are Topological Motifs?
The Topological Motif
Compact Topological Motifs
The Discovery Method
Related Classical Problems
Applications
Conclusion

SET-THEORETIC ALGORITHMIC TOOLS
Introduction
Some Basic Properties of Finite Sets
Partial Order Graph G(S,E) of Sets
Boolean Closure of Sets
Consecutive (Linear) Arrangement of Set Members
Maximal Set Intersection Problem (maxSIP)
Minimal Set Intersection Problem (minSIP)
Multi-Sets
Adapting the Enumeration Scheme

EXPRESSION AND PARTIAL ORDER MOTIFS
Introduction
Extracting (monotone CNF) Boolean Expressions
Extracting Partial Orders
Statistics of Partial Orders
Redescriptions
Application: Partial Order of Expressions
Summary

REFERENCES

INDEX

Exercises appear at the end of every chapter.