... Lakshmanan1
lakshman@nssl.noaa.gov 
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... candidate.2
A better representation, from the point of view of optimization using GAs, is each digit of the real and imaginary parts. Instead of using decimal numbers, one could also use the digits of the numbers to a base 2, i.e. the bits with which they are stored in computer memory. 
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... by:3
The probability distribution of $x_2$ given a value of $x_1$ is $1/(1-x_1)$ in the range $[x_1,1)$ and zero everywhere else. So, the probability that both $x_1$ and $x_2$ are less than a number $t$ is given by
\begin{displaymath} P( x_1 < t~~and~~x_2 < t ) = \int_{x_1=0}^t dx_1 \int_{x_2=x_1}^t \frac{dx_2}{1-x_1} \end{displaymath} (1)

which evaluates to $t + (1-t).log(1-t)$. Using Bayes Theorem and $P(x_1<t~\vert~x_2 < t) = 1$, we can evaluate $P(x_2<t)$. The median value of $x_2$ is the value of $x$ for which $P(x_2 < x) = 0.5$ and the probability distribution can be obtained from $P(x_2 < x)$ using:
\begin{displaymath} P_{x_2}(x) = \frac{d}{dx} P(x_2 < x) \end{displaymath} (2)

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....4
Since we generate random numbers in the range [0,1), $x_{max}$ should really be one $x_{quant}$ past the largest number that the underlying value can take. 
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... endorsements5
We also peg BWERs with confidences above 0.75 as having strong endorsements. These numbers are ad hoc, and could as well be 0.33 and 0.67. The GA will do its tuning according to whichever numbers are used. The important thing is that some detections are discarded using a crisp threshold and that the crisp threshold is consistent between the run-time and tuning cases. 
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... distance6
We define the distance,$d$, between two points $(x_1,y_1)$ and $(x_2,y_2)$ as $d = \vert x_1-x_2\vert + \vert y_1-y_2\vert$ rather than using the computationally more expensive Euclidean distance. 
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... integration7
The value of $\sigma$ can be obtained from the appendix of any engineering or statistics text if the value of $p_m$ is known beforehand. 
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... network.8
There was no particular rationale in deciding to use the Heidke Skill Score rather than the Critical Success Index - just that either one could be used, so we used both! In a rare-event situation, then Marzban (1998) derives the result that the CSI and HSS are optimized simultaneously. 
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