Biomedical subjects

Parongama Sen

Publications and source records attributed to Parongama Sen.

8 recordsLinked to original sources

PubMed2006

Phase transitions in an Ising model on a Euclidean network.

A one-dimensional network on which there are long-range bonds at lattice distances l>1 with the probability P(l) proportional to l(-delta) has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbors apart from their nearest neighbors for 0<or=delta<2. It is observed that there is a finite temperature phase transition in the entire range. For 0<or=delta<1, finite-size scaling behavior of various quantities are consistent with mean-field exponents while for 1<or=delta<or=2, the exponents depend on delta. The results are discussed in the context of earlier observations on the topology of the underlying network.

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PubMed2004

Phase transitions in an aging network.

We consider a growing network in which an incoming node gets attached to the ith existing node with the probability Pi(i) is proportional to ki(beta)taui(alpha)i , where ki is the degree of the ith node and taui its present age. The phase diagram in the alpha-beta plane is obtained. The network shows scale-free behavior, i.e., the degree distribution Pk approximately k(-gamma) with gamma=3 only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram.

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PubMed2004

Accelerated growth in outgoing links in evolving networks: deterministic versus stochastic picture.

In several real-world networks such as the Internet, World Wide Web, etc., the number of links grow in time in a nonlinear fashion. We consider growing networks in which the number of outgoing links is a nonlinear function of time but new links between older nodes are forbidden. The attachments are made using a preferential attachment scheme. In the deterministic picture, the number of outgoing links m (t) at any time t is taken as N (t)(theta) where N (t) is the number of nodes present at that time. The continuum theory predicts a power-law decay of the degree distribution: P (k) proportional to k-(1-2/ (1-theta ) ), while the degree of the node introduced at time t(i) is given by k(t(i),t)=t(theta)(i) [t/t(i) ]((1+theta)/2) when the network is evolved till time t. Numerical results show a growth in the degree distribution for small k values at any nonzero theta. In the stochastic picture, m (t) is a random variable. As long as is independent of time, the network shows a behavior similar to the Barabási-Albert (BA) model. Different results are obtained when is time dependent, e.g., when m (t) follows a distribution P (m) proportional to m(-lambda). The behavior of P (k) changes significantly as lambda is varied: for lambda>3, the network has a scale-free distribution belonging to the BA class as predicted by the mean field theory; for smaller values of lambda it shows different behavior. Characteristic features of the clustering coefficients in both models have also been discussed.

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PubMed2004

Scale-free network on a vertical plane.

A scale-free network is grown in the Euclidean space with a global directional bias. On a vertical plane, nodes are introduced at unit rate at randomly selected points and a node is allowed to be connected only to the subset of nodes which are below it using the attachment probability, pi(i)(t) approximately k(i)(t)l(alpha). Our numerical results indicate that the directed scale-free network for alpha=0 belongs to a different universality class compared to the isotropic scale-free network. For alpha - infinity. The link length distribution is calculated analytically for all values of alpha.

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PubMed2003

Clustering properties of a generalized critical Euclidean network.

Many real-world networks exhibit a scale-free feature, have a small diameter, and a high clustering tendency. We study the properties of a growing network, which has all these features, in which an incoming node is connected to its ith predecessor of degree k(i) with a link of length l using a probability proportional to k(beta)(i)l(alpha). For alpha>-0.5, the network is scale-free at beta=1 with the degree distribution P(k) proportional to k(-gamma) and gamma=3.0 as in the Barabási-Albert model (alpha=0,beta=1). We find a phase boundary in the alpha-beta plane along which the network is scale-free. Interestingly, we find a scale-free behavior even for beta>1 for alpha<-0.5, where the existence of a different universality class is indicated from the behavior of the degree distribution and the clustering coefficients. The network has a small diameter in the entire scale-free region. The clustering coefficients emulate the behavior of most real networks for increasing negative values of alpha on the phase boundary.

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PubMed2003

Small-world properties of the Indian railway network.

Structural properties of the Indian railway network is studied in the light of recent investigations of the scaling properties of different complex networks. Stations are considered as "nodes" and an arbitrary pair of stations is said to be connected by a "link" when at least one train stops at both stations. Rigorous analysis of the existing data shows that the Indian railway network displays small-world properties. We define and estimate several other quantities associated with this network.

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PubMed2002

Modulated scale-free network in Euclidean space.

A random network is grown by introducing at unit rate randomly selected nodes on the Euclidean space. A node is randomly connected to its ith predecessor of degree k(i) with a directed link of length l using a probability proportional to k(i)l(alpha). Our numerical study indicates that the network is scale free for all values of alpha>alpha(c) and the degree distribution decays stretched exponentially for the other values of alpha. The link length distribution follows a power law: D(l) approximately l(delta), where delta is calculated exactly for the whole range of values of alpha.

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PubMed2002

Phase transitions in a network with a range-dependent connection probability.

We consider a one-dimensional network in which the nodes at Euclidean distance l can have long range connections with a probability P(l) approximately l(-delta) in addition to nearest neighbor connections. This system has been shown to exhibit small-world behavior for delta<2, above which its behavior is like a regular lattice. From the study of the clustering coefficients, we show that there is a transition to a random network at delta=1. The finite size scaling analysis of the clustering coefficients obtained from numerical simulations indicates that a continuous phase transition occurs at this point. Using these results, we find that the two transitions occurring in this network can be detected in any dimension by the behavior of a single quantity, the average bond length. The phase transitions in all dimensions are nontrivial in nature.

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