where p:(i j corresponds to the pixel of column coordinate i and row coordinate j.
The output of DIALIGN is a mapping of the query sequence coordinates to various reference sequence coordinates (i.e. regions).
where (u, v) represents difference array coordinates, (i and j stand for original array coordinates, θ represents different directions (horizontal (h), vertical (v), diagonal (d), and minor diagonal (m)).
Finally, we need to place the iso-eccentricity coordinates, i.e., the green (inner 10∘) and blue (10∘ 90∘) coordinate lines in Fig. 2c.
The movement information (Δx,Δy) of the lattice in both screens can be calculated by the zero order of diffraction point coordinate (i.e., the center position).
Let p 1 : E × E → E denote the projection of the first coordinate, i.e., p 1 ( x, y ) = x for all x, y ∈ X.
Let us introduce a right-handed orthogonal curvilinear coordinate system {x1,x3} x3}, in which the field lines are along the x3 coordinate, i.e. lines along which the other two coordinates are invariable.
With the disparity map, the lower resolution frame I L,LR1 is warped geometrically by the corresponding full resolution frame I R. The value of one pixel at coordinate (i, j) in the full resolution frame is given in (6), where d i, j) is the disparity of pixel p at coordinate (i, j), I L,FR1 is the full resolution frame, I_{mathrm{L,FR1}}(i,j =I_{mathrm{R}}left(i+d i,j),jright).
The Weighted Histogram Analysis Method (WHAM) [42] was used to unbias the umbrella-sampling results along the RC2 reaction coordinate, i.e. along the glycosidic bond cleavage.
In the plot, the coordinate (i, j) in the lower diagonal where i > j (1 ≤ i, j ≤ 300) represents the gene overlap (X g ) between m i and m j, on the other hand, the coordinate (i, j) in the upper diagonal where i < j represents the sample overlap (X s ).
