Biomedical subjects

A Ramezanpour

Publications and source records attributed to A Ramezanpour.

6 recordsLinked to original sources

PubMed2006

Simplifying random satisfiability problems by removing frustrating interactions.

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.

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PubMed2005

Elastic properties of small-world spring networks.

We construct small-world spring networks based on a one-dimensional chain and study its static and quasistatic behavior with respect to external forces. Regular bonds and shortcuts are assigned linear springs of constant k and k', respectively. In our models, shortcuts can only stand extensions less than deltac beyond which they are removed from the network. First we consider the simple cases of a hierarchical small-world network and a complete network. In the main part of this paper we study random small-world networks (RSWN) in which each pair of nodes is connected by a shortcut with probability p. We obtain a scaling relation for the effective stiffness of RSWN when k=k'. In this case the extension distribution of shortcuts is scale free with the exponent -2. There is a strong positive correlation between the extension of shortcuts and their betweenness. We find that the chemical end-to-end distance (CEED) could change either abruptly or continuously with respect to the external force. In the former case, the critical force is determined by the average number of shortcuts emanating from a node. In the latter case, the distribution of changes in CEED obeys power laws of the exponent -alpha with alpha < or = 3/2.

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PubMed2005

Biased random satisfiability problems: from easy to hard instances.

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 alpha(c) proportional p(-(K-1)) for p --> 0. Solving numerically the survey propagation equations for K = 3 we find that for p < p* approximately 0.17 there is no replica symmetry breaking and still the SAT-UNSAT transition is discontinuous.

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PubMed2004

Ising model on the edge-dual of random networks.

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.

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PubMed2003

Generating correlated networks from uncorrelated ones.

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.

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PubMed2002

Simple models of small-world networks with directed links.

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.

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