The Rayleigh test [ 30] was employed to determine whether the sample of 22 mean directions (5 angles per individual; N = 22) differed significantly from random with respect to the mouse's trail (that is, the line between Ix,y and Sx,y).
However the actual mean direction of these angles is 0°, and the correct circular standard deviation is 1.4°.
If the secondary fODF peak had a smaller angle with the mean direction, the secondary fODF peak was chosen for the calculation of the OP instead.
If the secondary peak had a smaller angle with the mean direction, the secondary peak was chosen for the calculation of the OP instead.
The directed component specifies the mean angle that a theoretical pollen tube would turn in response to a gradient of the attractant, and the random component adds a random angle chosen from a Gaussian distribution to this mean direction.
Following image processing with our algorithm, available metrics to quantify neurite alignment include angular histograms, percent of neurite segments in a given direction, and mean neurite angle.
Interestingly, the mean direction vector that produces minimum correlation is at the mean elevation angles.
To test for differences in grain angle between circumferential direction (N, S, E, W), mean grain angle was calculated by direction and tree, and a two-way ANOVA fitted with terms for tree and direction.
The direction ⟨Δ θ⟩ of the angles is found by calculating the mean vector ⟨ u⟩: The mean direction ⟨Δ θ⟩ is apparent when ⟨ u⟩ is expressed in polar coordinates: In this expression ⟨Δ θ⟩ is the direction of the mean vector ⟨ u⟩ and thus the mean direction of the is population of angles {Δ θ i }.
The mean direction and the OP were then calculated for the direction that is more tangential (defined by the angle between the fODF peak and surface normal).
