Homework for APC/MOL 360

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Homework #1:

(2/17) [solutions]

 

Exercises 1.1, 1.2, 1.3, 1.4, 1.8, 1.9, 1.18

Computer Project 1.1, 1.2, 1.3, 1.5*

Homework #2

(2/24) [solutions]

 Homework #3

(3/3) [solutions]

Homework #4

(3/10) [ solutions]

 

Homework #5

(3/17) [solutions]  

 

Homework #6

(3/31) [solutions]

 

Homework #7

(4/7) [solutions]

 

Homework #8

(4/14) [solutions]

 

 

Homework #9

(4/21) [solutions]

 

 

Homework #10:

(4/28)

 

 

Exercise 6.5

 

Computer Project 6.1 [(i) Write a program to compute the relative prediction error as a function of the number of nearby points k, using an embedding dimension of p=1;

(ii*) Repeat part i for an arbitrary embedding dimension p.]

 

Problem 3:  The file HW10dat.mat contains seven time series in the variables D1, D2, D3, D4, D5, D6, and D7 .  Using the techniques learned in class, characterize the series according to whether they correspond to an underlying system that is deterministic, random, or some combination of the two.

(*) Find the time series that has an underlying chaotic attractor of dimension greater than 1.

 

 

Homework #11:

(5/5)

 

 

The file HW11.mat contains the data for this week's homework.

 

Problem 1:  The matrix X1 contains 200 measurements of the displacements of 100 nodes along a line.  Perform a principal components analysis to determine the 1st principal component, and the major direction of collective movement.  Characterize the behavior of the nodes.  Repeat for X2.

 

Problem 2:   The matrix Y1 contains the (synthetic) transcriptional responses of 2000 genes sampled at times t = 0, 10, 20, ... , 140.  Perform a singular value decomposition to determine the number of singular directions of collective expression of the genes.  Make a scatter plot of the data on the projections to the first and second eigengenes, and interpret the data.  Repeat for Y2.