Question 1:

Please finish up the fourier analysis on the data sets of last week if you did not get to them. In addition, there are two more data sets to try:

• Arctic Ocean Index
• Magnetic Polarity Data Column 1 is years before present; columns 2 and 3 are different kinds of indicators about field strength - run your time series analysis on both of them.

For both of these new data sets provide plots relevant to the fourier analysis



We are going to finish up the class with some material about machine learning. This represents a new topic not previously discussed and this week is a small exercise to start with, and then the larger exercise will be assigned next week and that will be do sometime during finals week

Machine learning comes in the guise of supervised or unsupervised learning and there are lots of resources to confuse you on the various aspects of machine learning.

Here we establish machine learning as fundamentally a simple process:

1. There is some initial state which is characterized by some computable parameter(s)
   
   
2. There is some final state, which is relatively close to the initial state (so the problem can be solved) in which the computable parameter has changed.
   
   
3. Randomly perturb the initial state and recalculate the parameter. If this parameter got closer to the final state then keep that perturbation. If not, then restore the pertubation back to the original state, but store that failure result so you will not repeat it.
   
   
4. Iterate through the above until the evolved perturbed state has the computable parameter close to the final state.

The above step procedure is likely mostly meaningless garble to you until you attempt to do a problem following this procedure and that is the problem given below.

Question 2:

1. Initial state is a square figure of size 10 x 10 pixels

2. Final state is a rectangular figure 14 pixels long (X) and 6 pixels wide (Y).

3. You iterate by randomly perturbing a pixel in the + or - X or Y directions by increment of one pixel.

4. You are to figure out your own rule set (computable parameters) that you need to compute to compare if the perturbation has produced something closer to or farther away from the final state . An obvious point should be that any random move in the +Y direction would be initially bad.

5. The principle output of this process is to print out the shape of the evolving figure every 10 iterations. This will also help you determine if your applied rule set is converging.

Note: I have given a problem like this to 3 professional programmers to see if its doable. It is, but is not as straighforward as you think, and that should be apparent. A couple of hints:

a) it is possible that you need to evolve your rule set

b) it is possible that you might have to work in absolute coordinate space to do this, but I hope not.