We study the behavior of solutions of mutually coupled equations in heterogeneous random graphs. Heterogeneity means that some equations receive many inputs whereas most of the equations are given only with a few connections. Starting from a situation where the isolated equations are unstable, we ...
GraphTheory[RandomGraphs] RandomGeometricGraph generate random geometric graph Calling Sequence Parameters Options Description Examples Compatibility Calling Sequence RandomGeometricGraph( n , t , dims , opts ) Parameters n - positive integer or list...
} The code is not particularly elegant or efficient but it does the job. At the very least it’s useful as a test baseline for the other solutions we’re going to come up with. Let’s follow Sean Parent’s dictum of“no raw loops”and see what else we can come up with. The poin...
large random regular graphs, the most striking being that 5-regular random graph with a threshold of activation of 3 (resp. 6-regular with threshold 4) have contagious sets containing a fraction1/6(resp.1/4) of the total number of vertices. Equivalently these numbers are the minimal fraction...
We focused on trees, since those are the simplest graphs, with the potential for having computable solutions as the literature review suggests. Second, we compute exactly the optimal control for some instances of this model. We proceed with an informal description of the model, then we high...
Both the even and odd solutions can be written in terms of as (33) or explicitly in terms of as (34) (35) The first few values of for , 1, ... are therefore 0, 1, 1, 3/2, 3/2, 15/8, 15/8, 35/16, 35/16, ... (OEIS A086116 and A060818; Abramowitz and Ste...
Such graphs are quite unlike real world networks, which often possess power-law or other highly skewed degree distributions. In this paper we study percolation on graphs with completely general degree distribution, giving exact solutions for a variety of cases, including site percolation, bond ...
Sly, Cutoff phenomena for random walks on random regular graphs, Duke Math. J. 153 (2010), no. 3, 475-510.LUBETZKY, E. and SLY, A. (2010). Cutoff phenomena for random walks on random regular graphs. Duke Math. J. 153 475-510. MR2667423...
Random geometric graphs in hyperbolic spaces explain many common structural and dynamical properties of real networks, yet they fail to predict the correct values of the exponents of power-law degree distributions observed in real networks. In that respect, random geometric graphs in asymptotically de...
If you are backing up logs properly as you should be you will also want to make sure you do not switch logs appreciably faster than you can back them up. Some backup solutions work more efficiently with larger logs. Testing The ideal test environment is a clone of your production system....