deletions | additions       diff --git a/results_table.tex b/results_table.tex  index 946231e..680bc1e 100644  --- a/results_table.tex  +++ b/results_table.tex 
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\]  where the last equation follows from the water hammer equations $dP_\pm = \pm \rho c dU_\pm$. Substituting these relationships into the ratio of the sum of squares  \[  \frac{\sum dP^2}{\sum dU^2} = (\rho c)^2 \frac{ \sum (dP_+^2 +2dP_+dP_- +dP_-)^2}{\sum (dP_-^2 - 2dP_+dP_- +dP_-)^2} = (\rho c)^2 \qquad {if,} \qquad \sum dP_+dP_- = 0 \]  where the sums are taken over an integral number of cardiac periods. The last condition is equivalent to requiring that the forward and backward changes in pressure are not correlated over the cardiac period. In the coronary arteries this assumption is difficult to defend since both the forward and backward waves are generated by the contraction of the myocardium and so some correlation of the two might be expected. We therefore look for an alternative method for estimating the local wave speed from the simultaneously measured pressure and velocity.