Finite-size corrections for networks with both area-preserving and area-increasing branching.
2008-09-12T00:30:04Z (GMT) by
<p>(A) As in <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1000171#pcbi-1000171-g003" target="_blank">Figure 3B</a>, we numerically determine the scaling exponent <i>α</i> by OLS regression within a group of artificial networks spanning roughly 8 orders of magnitude in body mass (blood volume). The exponent obtained from a group is plotted against the size of the smallest network in that group (as measured by the number of capillaries, <i>N</i><sub>cap,<i>S</i></sub>). Many groups are built by systematically increasing the size of the smallest network, resulting in the depicted graph. In all cases the branching ratio was <i>n</i> = 2. Black circles: numerical values. Red curve: analytical approximation, Equation 23. Green curve: Best fit to the shape of Equation 23, . (B) As in (A), except that each exponent is plotted against the number of levels <i>N<sub>S</sub></i> of the smallest network in the group from which it was determined. We display results obtained for a branching ratio <i>n</i> = 2 (black circles) and <i>n</i> = 3 (green circles). The red circles mark the predictions of the WBE model, since <i>N<sub>S</sub></i> = 25 for the smallest network (a shrew, meaning <i>N̅</i> = 24 plus 1 level for pulsatile flow) in the case of <i>n</i> = 2, and <i>N<sub>S</sub></i> = 16 for <i>n</i> = 3.</p>