Introduction
Ubiquity of Patterns
Motivations Form Biology
The Need for Rigor
Who Is a Reader of This Book?
The Fundamentals
Basic Algorithmics
Introduction
Graphs
(Minimum Spanning Tree)
(Steiner Tree)
(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
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