15-883 Midterm Exam

This exam is open book, open notes. You can even use the Web if you like. And you can ask me if you have questions about any of the problems, but you may not discuss the exam with anyone else.

You must type your answers; handwritten answers will not be accepted. You can hand in hardcopy at the start of class on March 7, or email your answers to dst@cs.cmu.edu.

1. What is the difference between ligand-gated ion channel receptors and G-protein coupled (metabotropic) receptors? Give a specific example of each kind, chosen from any of the papers you've read so far. How does each kind act, and how long do the effects last?

2. Marr defined three types of inhibition in his associative memory model of hippocampus. Describe each type, what purpose it served, and how it operated.

3. Assume an input space of size 20 units over which patterns appear with 5 out of 20 bits on. Assume an output space of size 1000 units, with each unit having a fan-in of 4. Show all details of your calculations:
   (a) How many distinct input patterns are there?

   (b) For a given input pattern, how many output units will have a non-zero input, on average?

   (c) What is the probability that an output unit will have exactly two hits?

   (d) Suppose we want the output vectors to have an average activity level (alpha) of 3.2 percent. Derive the proper threshold for the output units to achieve this result. Show all your work, and the final answer. (This can be done with pencil and paper, or by writing a little bit of code to do the calculations for you. If you choose to write code, include the source with your answer.)

   (e) This network will produce pattern separation, but not pattern completion. Why? What could you do to get pattern completion?

   A word of advice about computing the combinatorial "choose" function C(n,k). The formula for this is (n!)/[(k!)(n-k)!)]. However, if you code it this way, you will suffer floating point roundoff errors. A better way to compute this function is to calculate [n*(n-1)*...*(n-k+1)]/(k!). Or use Lisp or Scheme, so you can do the calculation using bignums instead of floats.

4. Compare the putative role of acetylcholine in the rat hippocampus with that of serotonin in Aplysia; what are the similarities and differences? (A couple of paragraphs should suffice.)

5. A rat repeatedly swims to a hidden platform in the Morris water maze from several starting locations. Later, back in its home cage, the rat dreams about its experiences.
   (a) What role do attractors play in this story?

   (b) Why, in the rat's dream, does it travel toward the platform, instead of from the platform to one of the start locations, or back and forth between the platform and the start locations? Describe the mechanism responsible.

   (c) What is the supposed purpose of this mental replay phenomenon?