These parameters include the resolution of the search grid used for the pseudorotation scan (i.e. the increment in P and ν max ) and the minimal and maximal contour levels used in the plots.
M, modality; x min and x max, minimal and maximal values of the working range (for continuous variables); M1 and M2, 2 modalities of CO2 concentration.
The normalization applied on both curves, theoretical and experimental, was obtained through this transformation <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0012383.e006.PNG" class= inline-graphic"/> where Ai represents the average cellular density at sample i, and min and max represent the minimal and maximal numerical value of the i row of < A>.
The resulting raw frequency profiles were normalized to fit into the [0, 1] interval so they can be compared directly: (1) N = (R − M i n ) / (M a x − M i n ) Were R and N are the raw and the normalised value respectively, while Min and Max are the minimal and the maximal raw count value of the individual profile.
Now, we claim that X min, X max are minimal and maximal solutions of equation (3.1), that is, if X ( t ) is any solution of equation (3.1) such that V 0 ≤ X ( t ) ≤ W 0, t ∈ [ 0, T ], then V 0 ≤ X min ≤ X ( t ) ≤ X max ≤ W 0, t ∈ [ 0, T ]. (3.9).
K min and K max denote the minimal and maximal value of k, respectively.
Then there exist maximal and minimal solutions Y max, Y min ∈ [ Y L, Y U ] for equation (3.2).
Then there exist maximal and minimal solutions X max, X min ∈ [ X L, X U ] for equation (3.1).
Maximal and minimal systolic pressures (Ps max and Ps min) and pulse pressures (Pp max and Pp min) were determined over a single respiratory cycle.
