deletions | additions       diff --git a/2_5_Proposed_algorithm_begin__.tex b/2_5_Proposed_algorithm_begin__.tex  index dc500c9..7f5bdd1 100644  --- a/2_5_Proposed_algorithm_begin__.tex  +++ b/2_5_Proposed_algorithm_begin__.tex 
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2.5 Proposed algorithm  \begin{enumerate}  \item measure Measure  pressure $P(t)$ and velocity $U(t)$ simultaneously at the same location in an artery. \item calculate Calculate  the differences $dP(t)$ and $dU(t)$, in our case by using a Savitzky-Golay differentiating filter. \item assume Assume  a value for the wave speed $c$ (and for the density of blood $/rho$). $\rho$).  \item calculate Calculate  $\rho cdU(t)$ and $dP_\pm(t) = \frac{1}{2}\big(dP(t) \pm \rho cdU(t)\big)$. \item estimate Estimate  the probability density functions $\phi(dP)$, $\phi(\rho cdU)$, $\phi(dP_+)$ and $\phi(dP_-)$ using a kernel density estimation method. \item calculate Calculate  $\phi(dP_+ \pm dP_-) = \phi(dP_+) \otimes \phi(\pm dP_-)$ by convolution. \item calculate Calculate  the entropies $H(dP)$, $H(\rho cdU)$, $H(dP_+ + dP_-)$ and $H(dP_+ - dP_-)$ \item calculate Calculate  the mean pdfs $\phi(M_P) = \frac{1}{2}\big(\phi(dP) + \phi(dP_+ + dP_-)\big)$ and $\phi(M_U) = \frac{1}{2}\big(\phi(\rho cdU) - \phi(dP_+ - dP_-)\big)$. \item calculate Calculate  the entropies $H(M_P)$ and $H(M_U)$. \item calculate Calculate  the Jensen-Shannon divergences $JS_P = H(M_P) - \frac{1}{2}\big(H(dP) + H(dP_+ + dP_-)\big)$ and \\and  $JS_U = H(M_U) - \frac{1}{2}\big(H(\rho cDU) + H(dP_+ - dP_-)\big)$. \item calculate Calculate  the sum of the Jensen-Shannon distances $\Delta = \sqrt{JS_P} + \sqrt{JS_U}$. \item plot Plot  the result, select another value of $c$ and repeat from step 4. \item determine Determine  the value of $c$ that givens the minimum value of $\Deltaa$. $\Delta$.  \end{enumerate}