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Homework
#1: (2/17)
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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* |
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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. |
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Homework
#11: (5/5)
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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. |
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