Model for Gene Network Analysis

It is envisaged that most complex naturally occurring networks are driven by small world networks. Thus, the model developed and implemented in this work is inspired from Boolean networks (Thomas and Kauffman, 2001a 2001b Silvescu and Honavar, 2001 Albert, 2004), weight matrices (Weaver et al, 1999 and Ando and Iba, 2001) and small world phenomenon (Milgram, 1967 Watts and Strogatz, 1998  

The model ensures a set of simple non-dominated networks (Pareto optimal) while minimizing the numbers of indirect links in the networks. The total number of indirect links is minimized to keep the network sparse (i.e., to keep the network simple). The model also maximizes the percentage difference between clustering coefficients to maintain one of the small world network (SWN) characteristic and minimizes the sum of squared errors to fit the experimental data. One of the constraints is included to ensure the minimum connectivity in all non dominated networks. The other constraint is included to make the L(avgshortestpath) nearly equal to log -if so that SWN characteristic can be ensured. Mathematically, the model (Ganta, 2007) is  

Step 2 Based on squared Pearson correlations define the neighborhood of each node. Generate some links (say, k = r-q) per node with highly correlated nodes in the neighborhood to form a population of directed networks, where 1 Ln(r) k r (Watts and Strogatz (1998)). 

Step 3 Insert random links to the randomly generated networks with random probability (p) such that a total of pxrxq links are further added. 

Step 4 Insert time delay links to the network based on shifted Pearson 

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