1 1

 0.5 0.5



 -0.5 -0.5

 1 ---1
 -1 -0.5 0 05 1 -1 -05 0 05 1


 50 50

 40 40

 30 30

 20 20

 10 10

 0 0
 0 10 20 30 40 50 0 10 20 30 40 50
 (I) (II)


Figure 3-5 Returns maps of the data for r = 1: (a) Flow; (b) Pressure; (I) Original data;
 (II) Test Set. For the test set, spontaneous breath is in red, mandatory in blue.

 Several trial and error tests have allowed us to determine a good embedding

dimension K=10 for the nonlinear models (see 3.4.1), allowing both acceptable prediction

result (enough depth at the input) and low enough input dimensionality (to allow for

acceptable computational constraints: every added dimension means another input weight

vector). The exact dimension required by the embedding theorem is not computed,

because it usually overestimates the minimal order of the model, and it is dependent on

the sampling rate [21].