Two paths π and π ′ in a 2-complex are equivalent if there is a finite sequence of paths π = π 0, π 1, …, π m = π ′, where for 1 ≤ i ≤ m, the path π i is obtained from π i − 1 either by inserting or deleting a pair e e − 1 of inverse edges or else by inserting or deleting a defining path for one of the 2-cells of the complex.
The inverse proportion edge stopping function in Equation (10) removes the noise in the large area efficiently, because its diffusion is the inverse function of the image gradient.
For weighted betweenness, the shortest paths are computed using the inverse of the edge weight since heavier edges should warrant greater flow (and hence higher betweenness).
Lower diversity of recruits could stem from lower diversity of seed rain24, but we found that seed diversity did not vary with distance to forest edge (inverse Simpson, Fig. 2a; exponentiated Shannon, Supplementary Figure 1a).
The inverse dependence of edge enhancement on X-ray effective energy is observed (2.8% for 30 kV Mo/Nb and 1.1% for 40 kV W/Al, at magnification 3 and source-to-detector distance 1.0 m).
We then assign the inverse of each edge cost to the noise variance as.
Equivalently, we can model the problem using the inverse graph whose edges denote non-compatible or interacting SNPs (i.e., SNPs whose associated primers incur at least one interaction) in which case the objective is to identify an independent set rather than a clique.
The shearlet decomposition has been successfully employed in many problems from applied mathematics and signal processing, including decomposition of operators [11], inverse problems [12, 13], edge detection [14 16], image separation [17], and image restoration [18 20].
Therefore, because small-world-ness linearly scales with network size, and degree is approximately constant, then S also has a simple inverse linear scaling with edge density.
0 indicates no assortativity, and scores between 0 and −1 indicate inverse assortativity in which edges have the tendency to connect nodes with different attributes (ibid).
