[Martin Taylor 950223 17:10]
In my message 950221 16:00, I gave a set of results for the probability that
an e-coli run will eventually get within a distance F times the initial
distance. As I noted this morning, these results were wrong, because I
entered the table with a value of M too high by a factor of 2. My colleague
has now given me the results of the simulation runs, and, Boy! does that
error ever make a difference. Here's the real stuff (I hope:-).
Dim F=0.99 0.98 0.95 0.90 0.80 0.70 0.60 0.50
4 43 40 34 27 14 6 3 1
8 39 35 25 14 2 0 0 0
16 34 27 13 1 0 0 0 0
32 27 17 1 0 0 0 0 0
64 17 4 0 0 0 0 0 0
For large dimensionality, not so encouraging as the numbers I mistakenly
sent out earlier.
ยทยทยท
============================
I've asked Dave to consider another problem, which is a direct attack on
the e-coli walk, which is a random walk until a step moves e-coli in a
favourable directionm and then a straight run until matters stop improving.
The question is to find the probability that an improvement ratio of F
will be attained in N steps in D dimensions, for different values of F
ranging up from 50%. I'll let you know what he says about it.
Martin