[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.

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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