This is an open book, take-home examination to be turned in by 9:00 a.m. Thursday, June 8.
Please verify that you have returned borrowed books.
1. Write a short essay (not more than 500-1000 words) on the “bit“ as a unit of information, emphasizing especially the conceptual and physical limitations innate in this concept and its application to biophysical problems. As a check list of some items which you might want to, but do not necessarily need to, consider in planning this assay you are offered the following topics; 1) The bit as a working tool in digital computer operation, 2) The smallest bit which is physically reliable and determinate 5) The relationship between the smallest bit and the entropy - nogentropy relationship. 4) The number of bits per second required to convoy a message in a given communication medium.
2. Show that you have at least superficial knowledge of the workings of at least one digital and one analog computer by outlining one simple problem that might appropriately be solved by each and explaining in rather specific detail how this problem would be programmed for each and how the machine would deal with it. While you could correctly answer this problem by outlining a problem to be done by adding machine and by slide rule, I would prefer that you restrict yourself to types of digital and analog computers more likely to go by those names, You need not use the same problem in the two cases.
3. Feedback and control systems
a) Diagram in some detail a biological control loop system in which you can identify long and short subsidiary feedback and can recognize their characteristic influences.
b) Outline the conditions which can cause a feedback system to become unstable and those which will make it erratic .
c) in a simple negative feedback system where nominal intrinsic gain is 500 and effective gain is 120~ calculate b the feedback and determine the effect on effective gain if m varies plus 10% and if b varies plus 10%.
d) Describe somewhat quantitatively some one biological transducer code.
4. You have undoubtedly consulted a number of texts, monographs, reviews and original scientific papers in conjunction with your biophysics studies this past quarter. List your ten favorites, explaining briefly the material for which each excels and for which you found it helpful.
5. To demonstrate that you have acquired a little skill in manipulating binary quantities, calculate from basic principles, i.e. without the use of tables, the cosine of 1/16 of a radian to an accuracy sufficient to exclude errors in excess of 1/10 of one percent, doing your work in binary and converting finally to decimal and checking with an ordinary table. Show your work!