The extension theory for the solution of generic transport problems defined by positive functions in the algebra of a given adjacency matrix is also developed.
There are many methods for solving this (e.g. [ 27- 30]); they generally attempt to construct a match as similar as possible, optimizing some measure of similarity under various constraints, to the three given adjacency matchings.
In light of these considerations, it can be helpful to have "targets" in mind, such as an expectation of what the mean ISA should approach for a given biological system, technology platform, and adjacency measure.
For a given G V,E) with n nodes and m links, we use a adjacency list to store the network graph G V,E).
We call GGN the network for a given comparison, which is obtained by taking the sum of the adjacency matrices of the two GSNs under analysis.
For a given graph (G = (V,E)) containing n nodes, let A be the adjacency matrix of G and (lambda) be the eigenvalue.
In this paper, an adjacency matrix is used herein to represent the interconnectivity for a given topology containing MBS Zones.
We now introduce the notion of a consensus network for given input adjacency matrices A(1), A(2),.... Intuitively, two nodes should be connected in a consensus network only if all of the input networks 'agree' on that connection.
Mathematically, it can be calculated easily as the sum of a given column in the adjacency matrix.
The total number of possible adjacencies (including telomeres) for n syntenic blocks is roughly 2 n, but in a given genome there are at most 2 n adjacencies and each adjacency conflicts with at most 4 nother adjacencies.
