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640:338 Discrete and Probabilistic Models in Biology - Spring 06
SYLLABUS
This is an ideal syllabus. If experience be a guide,
we shall probably not go so fast nor get to
some of the topics at the end.
- LECTURES 1--7: Mathematical Modeling in Population Genetics
Text: Chapters 1 and 3; review in Chapter 2 as needed.
Background biology: Mendelian Genetics; genes, alleles, loci, genotypes
Background probability: Random sampling, law of large numbers,
Bernoulli and binomial distributions.
Population genetics: Random mating models, infinite population models,
Hardy-Weinberg equilibrium;
Wright-Fisher and Moran models; models with selection and
adaptation;
difference equations.
- LECTURES 8--14: Probabilistic Analysis of DNA sequencing methods
TEXT: Chapter 4
Probability: geometric, exponential, Poisson, continuous random
variables, law of small numbers, Poisson processes
Models for coverage analysis (shotgun sequencing, anchors).
Restriction enzymes, Analysis of restriction enzyme digest libraries
- LECTURES 15--17:Markov chains and applications to population
genetics and biological sequences
Text: Chapter 5
Markov chains, transition matrices, invariant distributions;
Markov models for sequences.
- LECTURES 18-21: Maximum Likelihood Estimation
Text: Chapter 6
Likelihood functions, Maximum likelihood estimation, application
to sequence models, and alignment.
- LECTURES 22-25: Dynamic programming and application to
sequence alignment.
Text: Chapter 7
Elementary theory of dynamic programming, application to
global and local alignment of two sequences.
- LECTURES 26-28: Hidden Markov Models
Text:Chapter 8
Hidden Markov models, Forward and Viterbi algorithms;
Application to sequence alignment.