Summary: PHYS 597A, CMPSC 497E: Graphs and networks in sys-
Homework assignment 10, due Tuesday April 14
1. Read the review article "Control, exploitation and tolerance of in-
tracellular noise" by C.Rao, D.M. Wolf and A. P. Arkin. Write down three
questions or ideas that you had while reading it. Follow up on your questions
and let me know what you find.
2. Construct a network of four nodes, such that each node's in-degree is
one or two. Associate a Boolean rule to each node. Assume that each node's
state changes at the same time (synchronous update).
a) Determine analytically (by taking away time from the Boolean rules,
and solving the resulting system of equations) the fixed points of the system.
b) Map the state transitions in the system. Start with an initial state, and
update the state of the nodes for a sufficient number of steps for determining
the attractor. Then start from a state that was not encountered yet, and
repeat until all states were considered. Draw a state transition network in
which the nodes are the states of the system and the directed edges mean
that the state at the end of the edge follows from the state at the beginning of
the edge by updating the nodes once. How many attractors does the network