The JS distance between two frequency vectors P and Q is defined as (4) where (5) is the mean of P and Q, and KL P, M) is the Kullback – Leibler divergence (Kullback, 1987) between P and M defined as (6) The JS metric was also used by Sims et al. (2009) for their Feature Frequency Profile (FFP) approach.
The Jensen Shannon divergence (JSD) between two probability vectors P and Q is a bounded distance metric defined as JSD (P ‖ Q ) = 1 2 D k l (P ‖ M ) + 1 2 D k l (Q ‖ M ), (10 where M = 1 2 (P + Q ), and 0 ≤ JSD(P‖ Q) ≤ 1.
PPCA is closely related to factor analysis [24], in which a statistical model is used to describe the relation between the observed vector p t and the corresponding latent variables z t.
In order to derive a quantitative constraint on neural dynamics, we take as our starting point the correspondence between the population vector P v, and the tangential velocity vector of the hand v ({x58|Schwartz 1994}):.
The Bonferroni post test indicated that there was a significant difference between mice implanted with CHO-B3 and CHO-B3 R27aS) CHO-B3 R27aSCHO cells containing the emPty vector (P < 0.051), and pristane only (P < 0.01).
Then, for a pair of two genes g and g', we calculate the cosine of the angle between the corresponding vectors (P g and P g ') to obtain the pathway similarity between the two genes, as S gg ' KEGG = p g ⋅ p g ' P g P g ', where | P g | and | P g '| are the norms of the vectors P g and P g', respectively.
Repeated-measures ANOVA yielded a significant main effect of time (P < 0.05), but no significant effect of vector (P = 0.77) nor interaction between vector and time (P = 0.43).
Similarly, the repeated-measures ANOVA for the average night time activity level by month revealed no statistically significant differences between treatment groups (main effect of vector, P = 0.58, vector by month interaction, P = 0.99, Fig. 8C).
Vector p is the curl between normal vector n at the design load water line and vector i of the ship in the forward direction.
The initial objective function value, J 0, corresponds to the parameter vector p 0 used as initial guess in the optimizations, which is randomly selected between the bounds p L and p U. The only exception is benchmark B2, where p 0 is the parameter vector reported in the original publication.
