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A pair of voxel face hits, surrounding a vertex value exceeding the surface value are used to form a triangle.
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We propose an extension of the original Frink's approach based on a cell-to-vertex interpolation to compute vertex values with neighbour cell values.
Having data on the three vertices, the GPU goes through all pixels of a single polygon, while gradually changing (interpolating) vertex values from one vertex to another.
Though the reconstructed divergence field may be discontinuous from cell to cell, the norm of the differences between the vertex values of the reconstructed divergence for neighboring cells is minimized.
The spline regression model provides the advantage that, being more sensitive to the data, it is more useful when deriving vertex values.
We use a "triangulated irregular network-based linear interpolation using Delaunay triangulation" approach, where the interpolation is constructed by a linear interpolation of the vertex values from the corresponding triangulation simplex.
Corollary 2.5 Let T be a rooted tree and let f* vik) be an information functional such that <img src="http://journals.plos.org/plosone/article/asset?id=info?doi/10.1371/journal.pone.0003079.e030.PNG" class= inline-graphic"/> pV (vik) and p*(vik) denotes the vertex probability value (k-th vertex on the i-th level) regarding fV and f*.
A decorated tree is called a tree monomial whenever for each its internal vertex the values of the arrows beginning from it increase from the left to the right.
In our case, we use an information functional [25] [27] leading to vertex probability values that can be used to define a graph-theoretical matrix.
Thus, the metabolism of host-associated bacteria is sparser, and contains less 'hubs' (pathways with high connectivity), as shown by the smaller range of vertex degree values.
A 100,000-fold permutation test was used to estimate the significance of observed D and H, by shuffling the assignment of vertex property values.
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