arXiv subjects

Parongama Sen

Publications and source records attributed to Parongama Sen.

At least 91 records · Page 5Linked to original sources

arXiv2007

Effect of a static phase transition on searching dynamics

We consider a one dimensional Euclidean network which is grown using a preferential attachment. Here the $j$th incoming node gets attached to the $i$th existing node with the probability $Π_i \propto k_i {l}_{ij}^α$, where ${l}_{ij}$ is the Euclidean distance between them and $k_i$ the degree of the $i$th node. This network is known to have a static phase transition point at $α_c \simeq 0.5$. On this network, we employ three different searching strategies based on degrees or distances or both, where the possibility of termination of search chains is allowed. A detailed analysis shows that these strategies are significantly affected by the presence of the static critical point. The distributions of the search path lengths and the success rates are also estimated and compared for the different strategies. These distributions appear to be marginally affected by the static phase transition.

cond-mat.stat-mech↗

arXiv2007

A novel approach to study realistic navigations on networks

We consider navigation or search schemes on networks which are realistic in the sense that not all search chains can be completed. We show that the quantity $μ= ρ/s_d$, where $s_d$ is the average dynamic shortest distance and $ρ$ the success rate of completion of a search, is a consistent measure for the quality of a search strategy. Taking the example of realistic searches on scale-free networks, we find that $μ$ scales with the system size $N$ as $N^{-δ}$, where $δ$ decreases as the searching strategy is improved. This measure is also shown to be sensitive to the distintinguishing characteristics of networks. In this new approach, a dynamic small world (DSW) effect is said to exist when $δ\approx 0$. We show that such a DSW indeed exists in social networks in which the linking probability is dependent on social distances.

physics.soc-ph↗

arXiv2007

Dynamics of unvisited sites in presence of mutually repulsive random walkers

We have considered the persistence of unvisited sites of a lattice, i.e., the probability $S(t)$ that a site remains unvisited till time $t$ in presence of mutually repulsive random walkers. The dynamics of this system has direct correspondence to that of the domain walls in a certain system of Ising spins where the number of domain walls become fixed following a zero termperature quench. Here we get the result that $S(t) \propto \exp(-αt^β)$ where $β$ is close to 0.5 and $α$ a function of the density of the walkers $ρ$. The number of persistent sites in presence of independent walkers of density $ρ^\prime$ is known to be $S^\prime (t) = \exp(-2 \sqrt{\frac{2}π} ρ^\prime t^{1/2})$. We show that a mapping of the interacting walkers' problem to the independent walkers' problem is possible with $ρ^\prime = ρ/(1-ρ)$ provided $ρ^\prime, ρ$ are small. We also discuss some other intricate results obtained in the interacting walkers' case.

cond-mat.stat-mech↗

arXiv2006

Modelling temporal and spatial features of collaboration network

The collaboration network is an example of a social network which has both non-trivial temporal and spatial dependence. Based on the observations of collaborations in Physical Review Letters, a model of collaboration network is proposed which correctly reproduces the time evolution of the link length distributions, clustering coefficients, degree distributions and assortative property of real data to a large extent.

physics.soc-ph↗

arXiv2006

Earthquake aftershock networks generated on Euclidean spaces of different fractal geometry

According to some recent analysis (M. Baiesi and M. Paczuski, Phys. Rev. E {\bf 69}, 066106, 2004 \cite{maya1}) of earthquake data, aftershock epicenters can be considered to represent the nodes of a network where the linking scheme depends on several factors. In the present paper a model network of earthquake aftershock epicenters is proposed based on this scheme and studied on fractals of different dimensions. The various statistical features of this network, like degree, link length, frequency and correlation distributions are evaluated and compared to the observed data. The results are also found to be independent of the fractal geometry.

cond-mat.stat-mech↗

arXiv2006

Phase transitions in 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 $P(l) \propto l^{-δ}$ has been taken under consideration. We investigate the critical behavior of the Ising model on such a network where spins interact with these extra neighbours apart from their nearest neighbours for $0 \leq δ< 2$. It is observed that there is a finite temperature phase transition in the entire range. For $0 \leq δ< 1$, finite size scaling behaviour of various quantities are consistent with mean field exponents while for $1\leq δ\leq 2$, the exponents depend on $δ$. The results are discussed in the context of earlier observations on the topology of the underlying network.

cond-mat.stat-mech↗

arXiv2006

Complexities of social networks: A Physicist's perspective

The review is a survey of the present status of research in social networks highlighting the topics of small world property, degree distributions, community structure, assortativity, modelling, dynamics and searching in social networks.

physics.soc-ph↗

arXiv2006

Time evolution of link length distribution in PRL collaboration network

An important aspect of a Euclidean network is its link length distribution, studied in a few real networks so far. We compute the distribution of the link lengths between collaborators whose papers appear in the PhysicalReview Letters (PRL) in several years within a range of four decades. The distribution is non-monotonic; there is a peak at nearest neighbour distances followed by a sharp fall and a subsequent rise at larger distances. The behaviour of the statistical properties of the distribution with time indicates that collaborations might become distance independent in about thirty to forty years.

physics.soc-ph↗

arXiv2005

Zero temperature dynamics of Ising model on a densely connected small world network

The zero temperature quenching dynamics of the ferromagnetic Ising model on a densely connected small world network is studied where long range bonds are added randomly with a finite probability $p$. We find that in contrast to the sparsely connected networks and random graph, there is no freezing and an initial random configuration of the spins reaches the equilibrium configuration within a very few Monte Carlo time steps in the thermodynamic limit for any $p \ne 0$. The residual energy and the number of spins flipped at any time shows an exponential relaxation to equilibrium. The persistence probability is also studied and it shows a saturation within a few time steps, the saturation value being 0.5 in the thermodynamic limit. These results are explained in the light of the topological properties of the network which is highly clustered and has a novel small world behaviour.

cond-mat.stat-mech↗

arXiv2005

Modelling Aging Characteristics in Citation Networks

Growing network models with preferential attachment dependent on both age and degree are proposed to simulate certain features of citation network noted in \cite{red2}. In this directed network, a new node gets attached to an older node with the probability $\sim K(k)f(t)$ where the degree and age of the older node are $k$ and $t$ respectively. Several functional forms of $K(k)$ and $f(t)$ have been considered. The desirable features of the citation network can be reproduced with $K(k) \sim k^{-β}$ and $f(t) \sim \exp(αt)$ with $β=2.0$ and $α= -0.2$ and with simple modifications in the growth scheme.

physics.soc-ph↗

arXiv2005

Dynamical frustration in ANNNI model and annealing

Zero temperature quench in the Axial Next Nearest Neighbour Ising (ANNNI) model fails to bring it to its ground state for a certain range of values of the frustration parameter $κ$, the ratio of the next nearest neighbour antiferromagnetic interaction strength to the nearest neighbour one. We apply several annealing methods, both classical and quantum, and observe that the behaviour of the residual energy and the order parameter depends on the value of $κ$ strongly. Classical or thermal annealing is found to be adequate for small values of $κ$. However, neither classical nor quantum annealing is effective at values of $κ$ close to the fully frustrated point $κ=0.5$, where the residual energy shows a very slow algebraic decay with the number of MCS.

cond-mat.stat-mech↗

arXiv2004

Persistence and dynamics in ANNNI chain

We investigate both the local and global persistence behaviour in ANNNI (axial next-nearest neighour Ising) model. We find that when the ratio $κ$ of the second neighbour interaction to the first neighbour interaction is less than 1, $P(t)$, the probability of a spin to remain in its original state upto time $t$ shows a stretched exponential decay. For $κ> 1$, $P(t)$ has a algebraic decay but the exponent is different from that of the nearest neighbour Ising model. The global persistence behaviour shows similar features. We also conduct some deeper investigations in the dynamics of the ANNNI model and conclude that it has a different dynamical behaviour compared to the nearest neighbour Ising model.

cond-mat.stat-mech↗

arXiv2004

Directed Accelerated Growth: Application in Citation Network

In many real world networks, the number of links increases nonlinearly with the number of nodes. Models of such accelerated growth have been considered earlier with deterministic and stochastic number of links. Here we consider stochastic accelerated growth in a network where links are directed. With the number of out-going links following a power law distribution, the results are similar to the undirected case. As the accelerated growth is enhanced, the degree distribution becomes independent of the ``initial attractiveness'', a parameter which plays a key role in directed networks. As an example of a directed model with accelerated growth, the citation network is considered, in which the distribution of the number of outgoing link has an exponential tail. The role of accelerated growth is examined here with two different growth laws.

cond-mat.stat-mech↗

arXiv2004

Phase Transitions in an Aging Network

We consider a growing network in which an incoming node gets attached to the $i^{th}$ existing node with the probability $Π_i \propto {k_i}^βτ_i^α$, where $k_{i}$ is the degree of the $i^{th}$ node and $τ_i$ its present age. The phase diagram in the ${α-β}$ plane is obtained. The network shows scale-free behaviour, i.e., the degree distribution $P(k) \sim k^{-γ}$ with $γ=3$ only along a line in this plane. Small world property, on the other hand, exists over a large region in the phase diagram.

cond-mat.stat-mech↗

arXiv2004

Probability distribution of persistent spins in a Ising chain

We study the probability distribution $Q(n,t)$ of $n(t)$, the fraction of spins unflipped till time $t$, in a Ising chain with ferromagnetic interactions. The distribution shows a peak at $n=n_{max}$ and in general is non-Gaussian and asymmetric in nature. However for $n>n_{max}$ it shows a Gaussian decay. A data collapse can be obtained when $Q(n,t)/L^α$ versus $(n-n_{max})L^β$ is plotted with $α\sim 0.45$ and $β\sim 0.6$. Interestingly, $n_{max}(t)$ shows a different behaviour compared to $ = P(t)$, the persistence probability which follows the well-known behaviour $P(t)\sim t^{-θ}$. A quantitative estimate of the asymmetry and non-Gaussian nature of $Q(n,t)$ is made by calculating its skewness and kurtosis.

cond-mat.stat-mech↗

arXiv2004

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

In several real-world networks like the Internet, WWW etc., the number of links grow in time in a non-linear fashion. We consider growing networks in which the number of outgoing links is a non-linear 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 $N(t)^θ$ where $N(t)$ is the number of nodes present at that time. The continuum theory predicts a power law decay of the degree distribution: $P(k) \propto k^{-1-\frac{2} {1-θ}}$, while the degree of the node introduced at time $t_i$ is given by $k(t_i,t) = t_i^θ[ \frac {t}{t_i}]^{\frac {1+θ}{2}}$ when the network is evolved till time $t$. Numerical results show a growth in the degree distribution for small $k$ values at any non-zero $θ$. In the stochastic picture, $m(t)$ is a random variable. As long as $ $ is independent of time, the network shows a behaviour similar to the Barabási-Albert (BA) model. Different results are obtained when $ $ is time-dependent, e.g., when $m(t)$ follows a distribution $P(m) \propto m^{-λ}$. The behaviour of $P(k)$ changes significantly as $λ$ is varied: for $λ> 3$, the network has a scale-free distribution belonging to the BA class as predicted by the mean field theory, for smaller values of $λ$ it shows different behaviour. Characteristic features of the clustering coefficients in both models have also been discussed.

cond-mat.stat-mech↗

arXiv2003

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: $π_i(t) \sim k_i(t)\ell^α$. Our numerical results indicate that the directed scale-free network for $α=0$ belongs to a different universality class compared to the isotropic scale-free network. For $α< α_c$ the degree distribution is stretched exponential in general which takes a pure exponential form in the limit of $α\to -\infty$. The link length distribution is calculated analytically for all values of $α$.

cond-mat.stat-mech↗

arXiv2003

Clustering properties of a generalised critical Euclidean network

Many real-world networks exhibit scale-free feature, have a small diameter and a high clustering tendency. We have studied the properties of a growing network, which has all these features, in which an incoming node is connected to its $i$th predecessor of degree $k_i$ with a link of length $\ell$ using a probability proportional to $k^β_i \ell^α$. For $α> -0.5$, the network is scale free at $β= 1$ with the degree distribution $P(k) \propto k^{-γ}$ and $γ= 3.0$ as in the Barabási-Albert model ($α=0, β=1$). We find a phase boundary in the $α-β$ plane along which the network is scale-free. Interestingly, we find scale-free behaviour even for $β> 1$ for $α< -0.5$ where the existence of a new universality class is indicated from the behaviour 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 behaviour of most real networks for increasing negative values of $α$ on the phase boundary.

cond-mat.stat-mech↗