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Furthermore, the optimal STEM detector design can be derived for atom-counting using the expression for the probability of error.
For the probability of error and the ROC curves, we resort to MCS experiments to obtain the performance curves.
Deriving an analytic expression for the probability of error is always desirable, because it could help to analyze the behavior of the error.
The same results are obtained for the probability of error as it varies with the network lifetime, for a fixed delay for detection, which is shown in Figure 8, top right graph.
Similar evaluations can be done for the probability of error performances, and it can be seen in Figure 24 that the probability of error curves of CSFFE for ρ=0 and ρ=1 cases saturate to lower values than those of CSFFE in Figure 22.
Both encoding schemes are equivalent, since one can move from one to the other by applying Weyl's displacement operator (hat{D} alpha)) to both states.1 In the minimum-error approach, the theoretical minimum for the probability of error is given by the Helstrom formula for discriminating two pure states [20].
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Finally, the simulation results presented in [18] are extended with the rigorous analysis of the probability of error for the OSD schemes which also includes the analysis how to select the optimum decoding list.
By the late 1990s, phred quality scores [8] (see also [9]) had become established as a standard, highly accurate method for quantifying the probability of error at each nucleotide in a sequence.
Rx3: After receiving y 3 n, Rx3 finds a unique index m ^ ^ 3 for some index l ^ ^ such that y 3 n, w n m ^ ^ 3, l ^ ^ ∈ A ∈ n ( Y 3, W ). For large enough n, the probability of error can be made sufficiently small if R 3 + L ≤ I ( W ; Y 3 ).
However, for any given patient the probability of error in classifying the biopsy as a cancer could be as high as 0.49 (if the distributions of the measurements for cancer and normal tissues overlap).
Similar results are observed when comparing the probability of bit error for the two decoders and when comparing the probability of error for the other three example codes.
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