-
Tue 22 Jan: basic terminology from genetics, as needed from chapter 1;
Section 3.2: allele and gene frequencies, random mating; Section 3: one
gene/two allele models; basic iterations, state Hardy-Weinberg
-
Thu 24 Jan: continue Hardy-Weinberg; autosomal and sex-linked
chromosome cases
Homework problems for first week:
- Exercise 3.3.1 (Chapter 3, page 22)
- Exercise 3.3.2 (Chapter 3, page 22; one part already done in class)
- Exercises 3.3.4-3.3.7 (Chapter 3, page 23)
URL for solutions was sent by e-mail.
-
Tue 29 Jan: sex-linked chromosome case, solve using difference
equations by matrix approach (see additional
sets of notes on difference equations)
-
Thu 31 Jan: Continued X-chromosome case and difference equations. 3.3.5 mutations (skip section 3.3.6)
*** QUIZ #1 ***
Homework problems for second week:
URL for solutions for the first two problems was sent by e-mail.
For the last problem,
see
here
(this is a Maple script that shows solutions to the problems in the notes on
difference equations; eigenvalues and eigenvectors are shown there).
Note these typos in the solution: in the matrix problem, part (c), it
should be x1 and x2 instead of x and y respectively, and in the answers for Ex
3.3.12, part i, it should be v1 and v2 in the numerators, not u1 and u2.
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Tue 5 Feb: Continued discussion of mutation model.
3.3.7 Finite population models, as an introduction to Markov
chains. The Moran model.
-
Thu 7 Feb: Discussion of homework. More discussion of Moran model.
Justification of the Markov Chain update equation p(t+1)=p(t)P.
*** QUIZ #2 ***
Homework problems for weeks 3 and 4:
Please note: I listed together problems for weeks 3 and 4. Also, the list
includes some Wright-Fisher problems. These latter problems can be easily
done by reading the notes (it is quite similar to Moran), or you can wait
until we cover the material next Tuesday.
URL for solutions for the first two problems was sent by e-mail.
-
Tue 12 Feb:
Wright-Fisher model. Start discussing selection.
3.4.2/3 model with selection (later,
we return to section 3.4.1 on cobwebbing); derivation of model.
-
Thu 14 Feb:
Continue deriving selection model. Start describing cobwebbing.
-
Tue 19 Feb:
Analysis by cobwebing of model with selection.
(We skipped 3.4.4 mean fitness increase for model with selection.)
Start chapter 4: Introduction to shotgun sequencing.
-
Thu 21 Feb:
Clarke-Carbone formula, estimate number of contigs; stochastic lengths.
Homework problems for week 5
URL for solutions was sent by e-mail.
-
Tue 26 Feb:
Finished coverage problems.
-
Thu 28 Feb:
Restriction enzymes: introduction, binomial model.
Poisson approximation of binomial.
Homework problems for week 6
URL for solutions was sent by e-mail.
-
Tue 4 Mar:
Poisson model of number of cuts. Exponential interarrival times.
Discussion of sums of Poisson process (application to double digests) and
thinning (application to partial digests).
[Instructor at IMA Workshop. Class taught by Dr. Ocone.]
-
Thu 6 Mar:
Exam 1.
[Instructor at IMA Workshop. Exam proctored by Dr. Vera-Licona.]
Homework problems for week 7
URL for solutions was sent by e-mail.
-
Tue 11 Mar:
Examples of thinning and partial and double digests.
Residual and current life.
-
Thu 13 Mar:
(Skip coverage probabilities for digest libraries. Homework problems for that
section are optional.)
Start Markov Chains.
Markov chains and graphs. Path probabilities.
Multi-step transitions using powers of transition matrix.
Homework problems for week 8
URL for solutions was sent by e-mail.
Project to be handed-in on Tuesday after
break, instead of quiz today
Tue 18 Mar and Thu 20 Mar:
Spring Break
-
Tue 25 Mar:
More review of Markov processes, probabilities of paths, and graphs.
Calculation of equilibrium distributions for several examples, and writing
general solutions by using eigenvalues and eigenvectors. Discussion of
convergence in the acyclic case (Theorem 6 in notes), and examples where
convergence does not hold.
-
Thu 27 Mar:
Estimation of initial probabilities and transitions from sample data.
Another example: birth and death processes.
Jukes-Cantor model (URL for notes sent by email.)
Homework problems for week 9
URL for solutions was sent by e-mail.
-
Tue 1 Apr:
Continue equilibrium distributions.
Start chapter 6: the idea of a statistical hypothesis;
likelihood function.
(Illustrated with IID model for
coin tossing and IID sites model for DNA.)
click here for some notes
complementing the ones for Chapter 6 (maximum likelihood and Bayesian
estimation)
-
Thu 3 Apr:
ML and MAP estimation.
Homework problems for week 10
URL for solutions was sent by e-mail.
-
Tue 8 Apr:
Continue ML and MAP estimation.
-
Thu 10 Apr:
Hypothesis testing.
Homework problems for week 11
URL for solutions: just change "10" to "11" in the URL sent by e-mail
for the week-10 problems.
-
Tue 15 Apr:
Continue p-values; start likelihood ratio.
-
Thu 17 Apr:
Exam 2
*** what follows is to be updated as the semester proceeds ***
-
Tue 22 Apr:
(Chapter 7)
Scoring sequence alignments.
[note: instructor at IMA Workshop; class taught by Dr. Vera-Licona]
-
Thu 24 Apr:
Intro to dynamic programming, and applications to alignment.
[note: instructor at IMA Workshop; class taught by Dr. Vera-Licona]
Homework problems for week 13
Solutions:
problem 1,
problem 2,
problem 3.
-
Tue 29 Apr:
Finish alignment (example).
Go back to finishing Chapter 6:
Conjugate priors, exponential families.
Likelihood ratio, chi-squared distribution.
Testing for independence vs Markov.
-
Thu 1 May:
Hidden Markov Models?
Homework problem for HMM (only if covered):
Solution is here.
-
Thu 8 May:
Final exam, 4-7PM, Hill 116 (note room!)
-
Wed 14 May, 8AM to 11AM: this was the original exam date according to
the schedule.
The two students who have told me that they are not taking the exam on the
previous week must contact the math dept to make arrangements for the exam (on
any of Monday through Wednesday),
