These studies employed a version of PCA that optimized the variance of the measured contour of the cell, to obtain a reduced set of dominant components of cell shape changes during migration.
In mathematical domain, PCA successively optimizes the variance of a linear amalgamation of the initial predictor variables: (1) u q = argmax (Var (X u ) ), u t u = 1 conditional upon the constraint u i T S X u j = 0, for every 1 ≤ i ≤ j.
Additional constraints on Γ allow further reduction in model complexity, e.g., γ t, f being identical at night time, in order to optimize the variance-bias trade-off; we further comment on this in Section 5.
To optimize the bias-variance tradeoff, the elastic net [ 19, 20] has been proposed and is our choice of regression model (see Methods).
We constructed 64 different sequences optimizing the following criteria: As response variance across different experimental trials is relatively high, we applied the constraints that all stimulus types (V, H, VH, and B) should occur equally often (4 times within each 10-Hz sequence) and that every switch should occur equally often (once within each 10-Hz sequence).
Other variants like c- optimality (optimize estimation of a linear combination of parameters) or a- optimality (optimize the sum of individual variances of parameter estimates) exist, but these are less common and will not be covered here.
In particular, we are interested in optimizing the sampling time selection in order to minimize the variance of the parameter estimation error.
Second-phase sampling patterns optimizing the proposed criterion lead to predictions closer to the true image than when using the kriging variance as the main criterion.
This paper focuses on optimizing the performance of ejected droplets during flight, i.e., drop formation sequence and minimum flight time variance.
For both experiments, diagnostic plots for normality of the data-set and equality of the variance of the samples were checked and, when necessary, the data were transformed [square-root score) or Log10(score + 1)] to optimize the homogeneity of variance across the four groups.
