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A7, Due 11/21

1. Graph problems.

a) Design two graphs with five nodes each so that the first graph has a Hamiltonian path, and the second does not. Show what the gel electrophoresis results would look like if you used Adleman's method on each graph.
b) How would you use Adleman's method to determine the shortest path between any given pair of nodes in a given graph?
c) How would you use Adleman's method to determine whether the given graph is disconnected (contains at least two connected components)?

2. Remind yourself what the truth table for XOR is, then design a see-saw gate system to compute XOR. Show the network and also the strand diagrams, as in the figure for the OR and AND gates in the paper by Qian and Winfree. Devise ODEs for your XOR system and show that they have the right behavior for the four possible inputs to the system.

3. Read the following three documents

a) The description of the bioweapons convention. More info here and here.
b) The description of the DARPA living foundries program.
c) The description of DARPA's purpose, with which the living foundries program (and any other DARPA program) must comply.

Now write three paragraphs. The first paragraph should argue that the technologies and capabilities being developed by the living foundries program are in contradiction to the bioweapons convention. The second paragraph should argue that the program is not in contradiction to the convention. Be sure to carefully examine each article in the convention, and refer by name to those that are most relevant to your arguments. Finally, the third paragraph should critique the bioweapons convention itself. It was written in response the bioweapons of the 50's and 60's. Is it still relevant? Should it be updated? How?

Turn in A7 here: