| Popis: |
The problem of reliably detecting a known set ofn vectors of weight wi embedded in a heavily overlapped Patterson function Pi is investigated by a Monte-Carlo simulation based on searches of computer-generated random number sequences. Several formulations of the criterion of fit were compared. All were found to improve when the criterion was based on a subset of m “worst fitting” vectors as judged by a low value of (Pi/wi). The best criteria were Σ i = 1 m (wiPi)/Σ i =1 m w i 2 , withm ≈ (0.4−0.5)n, Σ i 1/m wi, withm ≈ 0.3n, and Σ i=1 m (wiPi) withm ≈ 0.7n. In each case the detectability of the embedded vectors wi increases with increasing Σ(w) in relation to Σ(N), the standard deviation of the overlaid noise. A related simulation of a Patterson search for non-crystallographic symmetry shows that for a given size of the non-crystallographically symmetric region, the detectability increases with the order (2-fold, 6-fold, 12-fold) of the symmetry. |
