PHYSICS · Multi-part · Fermi University Physics · Mathematical Methods for Physics · Computational Physics · Scientific programming for physicists
Scientific Computing for Physicists, Ch Minimisation with guarantees, with constraints and with randomness
Problem
Basin hopping on a cluster, run from 50 independently seeded starts at a fixed budget of hops, reaches the lowest known energy in 13 of them.
((a)) Report the success rate with its binomial standard error, and check whether the normal approximation behind that error is adequate.
((b)) A longer budget reaches the same energy in all 20 of 20 seeds. What does p^±p^(1−p^)/n give, and what should be reported instead?
((c)) A cheaper search reaches it in 1 of 30 seeds. Can the formula's uncertainty be trusted here, and what can still be reported?