ISBN-10: 3540241663

ISBN-13: 9783540241669

Edition: 2007

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Bioinformatics as a discipline arose out of the need to introduce order into the massive data sets produced by the new technologies of molecular biology: large-scale DNA sequencing, measurements of RNA concentrations in multiple gene expression arrays, and new profiling techniques in proteomics. As such, bioinformatics integrates a number of traditional quantitative sciences such as mathematics, statistics, computer science and cybernetics with biological sciences such as genetics, genomics, proteomics and molecular evolution. In this comprehensive textbook, Polanski and Kimmel present mathematical models in bioinformatics and they describe the biological problems that inspire the computer science tools used to handle the enormous data sets involved. The first part of the book covers the mathematical and computational methods, while the practical applications are presented in the second part. The mathematical presentation is descriptive and avoids unnecessary formalism, and yet remains clear and precise. Emphasis is laid on motivation through biological problems and cross applications. Each of the four chapters in the first part is accompanied by exercises and problems to support an understanding of the techniques presented. Each of the six chapters of the second part is devoted to some specific application domain: sequence alignment, molecular phylogenetics and coalescence theory, genomics, proteomics, RNA, and DNA microarrays. Each chapter concludes with a problems and projects section, to deepen the reader's understanding and to allow for the design of derived methods. Many of the projects involve publicly available software and/or Web-based bioinformatics depositories. Finally, the book closes with a thorough bibliography, reaching from classic research results to very recent findings, providing many pointers for future research. Overall, this volume is ideally suited for a senior undergraduate or graduate course on bioinformatics, with a strong focus on its mathematical and computer science background.
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Book details

List price: $89.95
Copyright year: 2007
Publisher: Springer
Publication date: 4/19/2007
Binding: Hardcover
Pages: 376
Size: 6.50" wide x 8.75" long x 0.75" tall
Weight: 1.738
Language: English

Andrzej Polanski is Professor at the Silesian University of Technology. Prior to this, he worked as a Post Doctoral Fellow at the University of Texas, Human Genetics Center, Houston USA (1996-1997) ans as a Visiting Professor at Rice University, Houston USA (2001-2003). His research interests are in bioinformatics, biomedical modeling and control, modern control and optimization theory. Marek Kimmel, Ph.D., is a Professor of Statistics at Rice University in Houston, TX, Professor in Department of Automatic Control, Silesian University of Technology in Gliwice, Poland, Professor of Biostatistics and Applied Mathematics (adj.) at M.D. Anderson Cancer Center in Houston, and a Professor of Biometry (adj.) at the School of Public Health of the University of Texas in Houston. He is heading the Rice Bioinformatics Group as well as the doctoral program in Statistical Genetics and Bioinformatics. Dr. Kimmel is a Fellow of the American Statistical Association. His principal interests are stochastic modeling of human disease (in particular lung cancer progression and screening), statistical and population genetics, biostatistics and bioinformatics.

The Genesis of Bioinformatics
Bioinformatics Versus Other Disciplines
Further Developments: from Linear Information to Multidimensional Structure Organization
Mathematical and Computational Methods
Why Mathematical Modeling?
Fitting Models to Data
Computer Software
Mathematical and Computational Methods
Probability and Statistics
The Rules of Probability Calculus
Independence, Conditional Probabilities and Bayes' Rules
Random Variables
Vector Random Variables
Marginal Distributions
Operations on Random Variables
Expectation and Moments of Random Variables
Probability-Generating Functions and Characteristic Functions
A Collection of Discrete and Continuous Distributions
Bernoulli Trials and the Binomial Distribution
The Geometric Distribution
The Negative Binomial Distribution
The Poisson Distribution
The Multinomial Distribution
The Hypergeometric Distribution
The Normal (Gaussian) Distribution
The Exponential Distribution
The Gamma Distribution
The Beta Distribution
Likelihood maximization
Binomial Distribution
Multinomial distribution
Poisson Distribution
Geometric Distribution
Normal Distribution
Exponential Distribution
Other Methods of Estimating Parameters: a Comparison
Example 1. Uniform Distribution
Example 2. Cauchy Distribution
Minimum Variance Parameter Estimation
The Expectation Maximization Method
The Derivations of the Algorithm
Examples of Recursive Estimation of Parameters by Using the EM Algorithm
Statistical Tests
The Idea
Parametric Tests
Nonparametric Tests
Type I and II statistical errors
Markov Chains
Transition Probability Matrix and State Transition Graph
Time Evolution of Probability Distributions of States
Classification of States
Stationary Distribution
Reversible Markov Chains
Time-Continuous Markov Chains
Markov Chain Monte Carlo (MCMC) Methods
Acceptance-Rejection Rule
Applications of the Metropolis-Hastings Algorithm
Simulated Annealing and MC3
Hidden Markov Models
Probability of Occurrence of a Sequence of Symbols
Backward Algorithm
Forward Algorithm
Viterbi Algorithm
The Baum-Welch algorithm
Computer Science Algorithms
Sorting and Quicksort
Simple Sort
String Searches. Fast Search
Easy Search
Fast Search
Index Structures for Strings. Search Tries. Suffix Trees
A Treelike Structure in Computer Memory
Search Tries
Compact Search Tries
Suffix Tries and Suffix Trees
Suffix Arrays
Algorithms for Searching Tries
Building Tries
Remarks on the Efficiency of the Algorithms
The Burrows-Wheeler Transform
Inverse transform
BW Transform as a Compression Tool
BW Transform as a Search Tool for Patterns
BW Transform as an Associative, Compressed Memory
Computational Complexity of BW Transform
Hashing functions for addressing variables
Statistics of Memory Access Time with Hashing
Inquiring About Repetitive Structure of Sequences, Comparing Sequences and Detecting Sequence Overlap by Hashing
Pattern Analysis
Feature Extraction
Linear Classifiers
Linear Classifier Functions and Artificial Neurons
Artificial Neural Networks
Support Vector Machines
K-means Clustering
Hierarchical Clustering
Dimensionality Reduction, Principal Component Analysis
Singular-Value Decomposition (SVD)
Geometric Interpretation of SVD
Partial-Least-Squares (PLS) Method
Parametric Transformations
Hough Transform
Generalized Hough Transforms
Geometric Hashing
Static Optimization
Convexity and Concavity
Constrained Optimization with Equality Constraints
Constrained Optimization with Inequality Constraints
Sufficiency of Optimality Conditions for Constrained Problems
Computing Solutions to Optimization Problems
Linear Programming
Quadratic Programming
Recursive Optimization Algorithms
Dynamic Programming
Dynamic Programming Algorithm for a Discrete-Time System
Tracing a Path in a Plane
Shortest Paths in Arrays and Graphs
Combinatorial Optimization
Examples of Combinatorial Optimization Problems
Time Complexity
Decision and Optimization Problems
Classes of Problems and Algorithms
Suboptimal Algorithms
Unsolved Problems
Sequence Alignment
Number of Possible Alignments
Dot Matrices
Scoring Correspondences and Mismatches
Developing Scoring Functions
Estimating Probabilities of Nucleotide Substitution
Parametric Models of Nucleotide Substitution
Computing Transition Probabilities
Fitting Nucleotide Substitution Models to Data
Breaking the Loop of Dependencies
Scaling Substitution Probabilities
Amino Acid Substitution Matrices
Sequence Alignment by Dynamic Programming
The Needleman-Wunsch Alignment Algorithm
The Smith-Waterman Algorithm
Aligning Sequences Against Databases
Methods of Multiple Alignment
Molecular Phylogenetics
Trees: Vocabulary and Methods
The Vocabulary of Trees
Overview of Tree-Building Methodologies
Distance-Based Trees
Tree-Derived Distance
Ultrametric Distances and Molecular-Clock Trees
Unweighted Pair Group Method with Arithmetic Mean (UPGMA) Algorithm
Neighbor-Joining Trees
Maximum Likelihood (Felsenstein) Trees
Hypotheses and Steps
The Pulley Principle
Estimating Branch Lengths
Estimating the Tree Topology
Maximum-Parsimony Trees
Minimal Number of Evolutionary Events for a Given Tree
Searching for the Optimal Tree Topology
Miscellaneous Topics in Phylogenetic Tree Models
The Nonparametric Bootstrap Method
Variable Substitution Rates, the Felsenstein-Churchill Algorithm and Related Methods
The Evolutionary Trace Method and Functional Sites in Proteins
Coalescence Theory
Neutral Evolution: Interaction of Genetic Drift and Mutation
Modeling Genetic Drift
Modeling Mutation
Coalescence Under Different Demographic Scenarios
Statistical Inference on Demographic Hypotheses and Parameters
Markov Chain Monte Carlo (MCMC) Methods
Approximate Approaches
The DNA Molecule and the Central Dogma of Molecular Biology
Genome Structure
Genome Sequencing
Restriction Enzymes
Southern Blot
The Polymerase Chain Reaction
DNA Cloning
Chain Termination DNA Sequencing
Genome Shotgun Sequencing
Genome Assembly Algorithms
Growing Contigs from Fragments
Detection of Overlaps Between Reads
Repetitive Structure of DNA
The Shortest Superstring Problem
Overlap Graphs and the Hamiltonian Path Problem
Sequencing by Hybridization
De Bruijn Graphs
All l-mers in the Reads
The Euler Superpath Problem
Further Aspects of DNA Assembly Algorithms
Statistics of the Genome Coverage
Contigs, Gaps and Anchored Contigs
Statistics with Minimum Overlaps Between Fragments, Anchored Contigs
Genome Length and Structure Estimation by Sampling l-mers
Genome Annotation
Research Tools for Genome Annotation
Gene Identification
DNA Motifs
Annotation by Words and Comparisons of Genome Assemblies
Human Chromosome 14
Protein Structure
Amino Acids
Peptide Bonds
Primary Structure
Secondary Structure
Tertiary Structure
Quaternary Structure
Experimental Determination of Amino Acid Sequences and Protein Structures
Protein 2D Gels
Protein Western Blots
Mass Spectrometry
Chemical Identification of Amino Acids in Peptides
Analysis of Protein 3D Structure by X Ray Diffraction and NMR
Other Assays for Protein Compositions and Interactions
Computational Methods for Modeling Molecular Structures
Molecular-Force-Field Model
Molecular Dynamics
Hydrogen Bonds
Computation and Minimization of RMSD
Solutions to the Problem of Minimization of RMSD over Rotations
Solutions to the Problem of Minimization of RMSD over Rotations and Translations
Solvent-Accessible Surface of a Protein
Computational Prediction of Protein Structure and Function
Inferring Structures of Proteins
Protein Annotation
De Novo Methods
Comparative Modeling
Protein-Ligand Binding Analysis
Classification Based on Proteomic Assays
The RNA World Hypothesis
The Functions of RNA
Reverse Transcription, Sequencing RNA Chains
The Northern Blot
RNA Primary Structure
RNA Secondary Structure
RNA Tertiary Structure
Computational Prediction of RNA Secondary Structure
Nested Structure
Maximizing the Number of Pairings Between Bases
Minimizing the Energy of RNA Secondary Structure
Prediction of RNA Structure by Comparative Sequence Analysis
DNA Microarrays
Design of DNA Microarrays
Kinetics of the Binding Process
Data Preprocessing and Normalization
Normalization Procedures for Single Microarrays
Normalization Based on Spiked-in Control RNA
RMA Normalization Procedure
Correction of Ratio-Intensity Plots for cDNA
Statistics of Gene Expression Profiles
Modeling Probability Distributions of Gene Expressions
Class Prediction and Class Discovery
Dimensionality Reduction
Example of Application of PCA to Microarray Data
Class Discovery
Hierarchical Clustering
Class Prediction. Differentially Expressed Genes
Multiple Testing, and Analysis of False Discovery Rate (FDR)
FDR analysis in ALL versus AML gene expression data
The Gene Ontology Database
Structure of GO
Other Vocabularies of Terms
Supporting Results of DNA Microarray Analyses with GO and other Vocabulary Terms
Bioinformatic Databases and Bioinformatic Internet Resources
Genomic Databases
Proteomic Databases
RNA Databases
Gene Expression Databases
Ontology Databases
Databases of Genetic and Proteomic Pathways
Programs and Services
Clinical Databases
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