Syllabus for 640:338
To be updated during semester
Tue 18 Jan: basic terminology from genetics, as needed from chapter 1;
Section 3.2: allele and gene frequencies, random mating
Thu 20 Jan: Section 3.3, one gene/two allele models; basic iterations,
Tue 25 Jan: continued H-W; autosomal and sex-linked chromosome cases
Thu 27 Jan: continued sex-linked chromosome case (pp 23-24), but with
matrix approach (see also two additional sets of notes on difference
Tue 1 Feb: 3.3.5 mutations; 3.3.7 Wright-Fisher, introducing Markov
Chains (see Maple example worked out)
Thu 3 Feb: continuation
Tue 8 Feb: Moran model (page 33)
Thu 10 Feb:
3.4.2/3 model with selection (later
we come back to 3.4.1 cobwebbing); derivation of model.
Quiz 1: frequencies, monecious and diecious populations, X chromosome case
Tue 15 Feb: analysis by cobwebing of model with selection
Thu 17 Feb: 3.4.4 mean fitness increase for model with selection.
Chapter 4: coverage in shotgun sequencing, Clarke-Carbon
Tue 22 Feb: continue coverage in shotgun sequencing. Quiz2/3 (double quiz): matrix solutions of for linear difference
equations, mutations, Wright-Fisher (using Markov chains) and Moran, model
with selection, cobwebbing.
Thu 24 Feb: estimate number of contigs;
stochastic model for lengths Li in sequencing.
Tue 1 Mar:
finish stochastic model for lengths Li in sequencing; start restriction enzymes
Thu 3 Mar: Continue restriction enzymes. Poisson approximation of
Tue 8 Mar:
Class officially cancelled because of snow (university closure).
Thu 10 Mar: Exam 1.
Tue 15 Mar:
Thu 17 Mar:
Tue 22 Mar:
Poisson model of number of cuts. Exponential lengths. Thining.
Partial and double digests.
Thu 24 Mar:
Residual and current life. Coverage probabilities for digest libraries.
Tue 29 Mar:
Characterization of Poisson processes (extra notes). Start Markov chains.
Thu 31 Mar:
Markov chains and graphs. Path probabilities.
Tue 5 Apr:
Multi-step transitions using powers of transition matrix.
Start equilibrium distributions.
Thu 7 Apr:
Continue equilibrium distributions.
Jukes-Cantor model for DNA evolution based on Markov chains. (Scanned section
from a textbook.)
Tue 12 Apr:
(Class taught by Prof Ocone.)
Chapter 6. The idea of a statistical hypothesis.
The likelihood function, maximum likelihood estimates.
(Illustrated with IID model for
coin tossing and IID sites model for DNA.)
Thu 14 Apr:
Finish Jukes-Cantor, and mention Kimura model (from scan).
Tue 19 Apr:
Likelihood ratio, chi-squared distribution.
Thu 21 Apr:
Testing for independence vs Markov. Scoring sequence alignments.
1/2 hour test (Poisson models for restriction enzymes, partial and double
digests, Markov Chains)
Tue 26 Apr:
Continue scoring sequence alignments; start
intro to dynamic programming, and applications to alignment.
Thu 28 Apr:
Continue dynamic programming and applications to alignment.
1/2 hour test (Markov chains, max likelihood estimation, hypothesis testing)
Wed 11 May, 4:00PM to 7:00PM: final exam (tentative)
VERY PROBABLY A TAKE-HOME.