Sharif Digital Repository

In this work we study a simple evolutionary model of bipartite networks whose evolution is based on the duplication of nodes. Using analytical results along with numerical simulation of the model, we show that the above evolutionary model results in weighted scalefree networks. Indeed we find that in the one-mode picture we have weighted networks with scale-free distributions for interesting quantities like the weights, the degrees and the weighted degrees of the nodes and the weights of the edges  

The Ising model with nearest-neighbor interactions on the edge dual of uncorrelated random networks was discussed. It was found that in the thermodynamic limit, the networks have a finite clustering. Low- and high-temperature expansions of Ising model on the edge dual of random networks were derived. A comparison of the critical behavior of Ising model on scale free random networks and their edge dual was performed. A simple relation was given between the partition function of an Ising model with nearest- and next-nearest-neighbor interactions on a tree like network and its edge dual  

We consider the Ising model on the edge dual of uncorrelated random networks with arbitrary degree distribution. These networks have a finite clustering in the thermodynamic limit. High- and low-temperature expansions of Ising model on the edge dual of random networks are derived. A detailed comparison of the critical behavior of Ising model on scale free random networks and their edge dual is presented. © 2004 The American Physical Society  

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 [formula presented] 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... 

We consider an interacting system of spin variables on a loopy interaction graph, identified by a tree graph and a set of loopy interactions. We start from a high-temperature expansion for loopy interactions represented by a sum of non-negative contributions from all the possible frustration-free loop configurations. We then compute the loop corrections using different approximations for the nonlocal loop interactions induced by the spin correlations in the tree graph. For distant loopy interactions, we can exploit the exponential decay of correlations in the tree interaction graph to compute loop corrections within an independent-loop approximation. Higher orders of the approximation are... 

Working with tree graphs is always easier than with loopy ones and spanning trees are the closest tree-like structures to a given graph. We find a correspondence between the solutions of random K-satisfiability problem and those of spanning trees in the associated factor graph. We introduce a modified survey propagation algorithm which returns null edges of the factor graph and helps us to find satisfiable spanning trees. This allows us to study organization of satisfiable spanning trees in the space spanned by spanning trees. © 2006 IOP Publishing Ltd  

How can we remove some interactions (generate shorter clauses) in a constraint satisfaction problem (CSP) such that it still remains satisfiable? In this paper we study a modified survey propagation algorithm that enables us to address this question for a prototypical CSP, i.e., random K -satisfiability problem. The average number of removed interactions is controlled by a tuning parameter in the algorithm. If the original problem is satisfiable then we are able to construct satisfiable subproblems ranging from the original one to a minimal one with minimum possible number of interactions. The minimal satisfiable subproblems will directly provide the solutions of the original problem. © 2006... 

In this paper we study biased random K-satisfiability (K-SAT) problems in which each logical variable is negated with probability p. This generalization provides us a crossover from easy to hard problems and would help us in a better understanding of the typical complexity of random K-SAT problems. The exact solution of 1-SAT case is given. The critical point of K-SAT problems and results of replica method are derived in the replica symmetry framework. It is found that in this approximation αcp-(K-1) for p→0. Solving numerically the survey propagation equations for K=3 we find that for p