deletions | additions       diff --git a/Because_I_is_calculated_from__.tex b/Because_I_is_calculated_from__.tex  index 47c2390..93011e2 100644  --- a/Because_I_is_calculated_from__.tex  +++ b/Because_I_is_calculated_from__.tex 
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--------------------- edited to here ----------------------  Because $I$ is calculated from probability density functions that are estimated from the histograms, the results are sensitive to the number and the size of the bins used to calculate the histograms. For a small number of bins, there are a large number of samples in each bin and so the approximation to the underlying probability is better. At the same time, there are fewer values of $X$ and $Y$ and so the mutual information decreases. This can be seen most easily in the values of $I(P,P)$, $I(U,U)$ and $I(P,U)$ indicated by the horizontal dashed lines. We also observe that the value of $c$ for which $I(dP_+,dP_-)$ indicated by the red circle is minimum tends is constant for a relatively small number of bins but begins to increase when the number of bins increases. The constancy of the value of $c$ for which $I$ is minimum For a small number of bins (bins < 256) indicates that there may be an algorithm for determining the appropriate bin size for any particular measurement that will result in a robust estimate of $c$. In this particular example $c_{MI}$ is only slightly larger than $c_{SS}$.