生物信息學(xué)中的數(shù)學(xué)方法引論

內(nèi)容概要

This book looks at the mathematical foundations of the models
currently in use. This is crucial for the correct interpretation of
the outputs of the models. A bioinformatician should be able not
only to use software packages, but also to know the mathematics
behind these packages. From this point of view, mathematics
departments throughout the world have a major role to play in
bioinformatics education by teaching courses on the mathematical
foundations of the subject. Based on the courses taught by the
author the book combines several topics in biological sequence
analysis with mathematical and statistical material required for
such analysis.

書籍目錄

part i sequence analysis
　1 introduction: biological sequences
　2 sequence alignment
　2.1 sequence similarity
　2.2 dynamic programming: global alignment
　2.3 dynamic programming: local alignment
　2.4 alignment with affine gap model
　2.5 heuristic alignment algorithms
　2.5.1 fasta
　2.5.2 blast
　2.6 significance of scores
　2.7 multiple alignment
　2.7.1 msa
　2.7.2 progressive alignment
　exercises
　3 markov chains and hidden markov models
　3.1 markov chains
　3.2 hidden markov models
　3.3 the viterbi algorithm
　3.4 the forward algorithm
　3.5 the backward algorithm and posterior decoding
　3.6 parameter estimation for hmms
　3.6.1 estimation when paths are known
　3.6.2 estimation when paths are unknown
　3.7 hmms with silent states
　3.8 profile hmms
　3.9 multiple sequence alignment by profile hmms
　exercises
　protein folding
　4.1 levels of protein structure
　4.2 prediction by profile hmms
　4.3 threading
　4.4 molecular modeling
　4.5 lattice hp-model
　exercises
　5 phylogenetic reconstruction
　5.1 phylogenetic trees
　5.2 parsimony methods
　5.3 distance methods
　5.4 evolutionary models
　5.4.1 the jukes-cantor model
　5.4.2 the kimura model
　5.4.3 the felsenstein model
　5.4.4 the hasegawa-kishino-yano (hky) model
　5.5 maximum likelihood method
　5.6 model comparison
　exercises
part ii mathematical background for sequence analysis
　6 elements of probability theory
　6.1 sample spaces and events
　6.2 probability measure
　6.3 conditional probability
　6.4 random variables
　6.5 integration of random variables
　6.6 monotone functions on the real line
　6.7 distribution functions
　6.8 common types of random variables
　6.8.1 the discrete type
　6.8.2 the continuous type
　6.9 common discrete and continuous distributions
　6.9.1 the discrete case
　6.9.2 the continuous case
　6.10 vector-valued random variables
　6.11 sequences of random variables
　exercises
　7 significance of sequence alignment scores
　7.1 the problem
　7.2 random walks
　7.3 significance of scores
　exercises
　elements of statistics
　8.1 statistical modeling
　8.2 parameter estimation
　8.3 hypothesis testing
　8.4 significance of scores for global alignments
　exercises
　9 substitution matrices
　9.1 the general form of a substitution matrix.
　9.2 pam substitution matrices
　9.3 blosum substitution matrices
　exercises
references
index

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