Assignment 1.

This is a hand calculation exercise to help familiarize you with some of the most basic computational properties of the brain. You may need to do some hunting in books or the WWW for numbers.

a) What is the minimum time interval between firings of cortical neurons? What is the minimum time for a person to give a forced choice response to a simple stimulus? How do these facts yield the intuitive hundred-step-rule of neural computation? Does the speed of neural signal transmission change the intuition?

b) About how many neurons are in the human brain? What is the fan-out of cortical neurons? From these two numbers, estimate the minimum number of links to reach all cortical neurons from some starting cell.

c) About how many base pairs are there in the human genetic code? About how many synapses are there in the brain?

The significant difference in these two values has been taken to prove that the genetic code could not specify all of our neural connections. Show that this argument fails if one takes into account the fact that much of cortex is laid out in systematic maps with regular connection patterns. Make a quantitative argument about how many bits would suffice.

Can you think of a biologically plausible way for the wiring to be done during development? Provide other arguments that neural connectivity is not fully specified in the genetic code, although it could be in principle.

d) Solve problem 2.13 in the Ballard book. Do these ideas provide any additional insights for problem c above?

If you don't have the book, the problem says:

13. Consider a problem in tactile sensing in which a stimulus is signaled by its position in an n * n two-dimensional grid. (Figure in book)

a. How many bits are needed to represent the code?

b. What is its information content?

Now consider the altrenative strategy of representing the signals with three overlapping sensory grids of (n/3)(n/3) sensors that are offset from each other by one unit (another Figure).

c. How many bits are needed to represent the code?

d. What is its information content

e. what is the savings of the second strategy over the first?

f. What advantage does the first strategy have over the second?

This assignment is due in class on Thursday, September 4 or by earlier
electronic submission.