Biomedical subjects
Publications and source records attributed to V Karimipour.
Given an ensemble of random graphs with a specific degree distribution, we show that the transformation which converts these graphs to their line (edge-dual) graphs produces an ensemble of graphs with nearly the same degree distribution, but with degree correlations and a much higher clustering coefficient. We also study the percolation properties of these new graphs.
We consider general multispecies models of reaction diffusion processes and obtain a set of constraints on the rates which give rise to closed systems of equations for correlation functions. Our results are valid in any dimension and on any type of lattice. We also show that under these conditions the evolution equations for two point functions at different times are also closed. As an example we introduce a class of two species models that may be useful for the description of voting processes or the spreading of epidemics.
We investigate the effect of directed short- and long-range connections in a simple model of a small-world network. Our model is one in which we can determine many quantities of interest by an exact analytical method. We calculate the function V(T), defined as the number of sites affected up to time T when a naive spreading process starts in the network. As opposed to shortcuts, the presence of unfavorable bonds has a negative effect on this quantity. Hence, the spreading process may not be able to affect all of the network. We define and calculate a quantity identified as the average size of the accessible world in our model. The interplay of shortcuts and unfavorable bonds on the small world properties is studied.
We analyze the effect of correlations in a simple model of a small-world network by obtaining exact analytical expressions for the distribution of shortest paths in the network. We enter correlations into a simple model with a distinguished site, by taking the random connections to this site from an Ising distribution. Our method shows how the transfer-matrix technique can be used in the new context of small-world networks.