arXiv subjects

S. S. Manna

Publications and source records attributed to S. S. Manna.

At least 37 records · Page 2Linked to original sources

arXiv2013

Information sharing and sorting in a community

We present the results of detailed numerical study of a model for the sharing and sorting of informations in a community consisting of a large number of agents. The information gathering takes place in a sequence of mutual bipartite interactions where randomly selected pairs of agents communicate with each other to enhance their knowledge and sort out the common information. Though our model is less restricted compared to the well established naming game, yet the numerical results strongly indicate that the whole set of exponents characterizing this model are different from those of the naming game and they assume non-trivial values. Finally it appears that in analogy to the emergence of clusters in the phenomenon of percolation, one can define clusters of agents here having the same information. We have studied in detail the growth of the largest cluster in this article and performed its finite-size scaling analysis.

physics.soc-ph↗

arXiv2011

Conservative self-organized extremal model for wealth distribution

We present a detailed numerical analysis of the modified version of a conservative self-organized extremal model introduced by Pianegonda et. al. for the distribution of wealth of the people in a society. Here the trading process has been modified by the stochastic bipartite trading rule. More specifically in a trade one of the agents is necessarily the one with the globally minimal value of wealth, the other one being selected randomly from the neighbors of the first agent. The pair of agents then randomly re-shuffle their entire amount of wealth without saving. This model has most of the characteristics similar to the self-organized critical Bak-Sneppen model of evolutionary dynamics. Numerical estimates of a number of critical exponents indicate this model is likely to belong to a new universality class different from the well known models in the literature. In addition the persistence time, which is the time interval between two successive updates of wealth of an agent has been observed to have a non-trivial power law distribution. An opposite version of the model has also been studied where the agent with maximal wealth is selected instead of the one with minimal wealth, which however, exhibits similar behavior as the Minimal Wealth model.

q-fin.GN↗

arXiv2011

About the fastest growth of Order Parameter in Models of Percolation

Can there be a `Litmus test' for determining the nature of transition in models of percolation? In this paper we argue that the answer is in the affirmative. All one needs to do is to measure the `growth exponent' $χ$ of the largest component at the percolation threshold; $χ< 1$ or $χ= 1$ determines if the transition is continuous or discontinuous. We show that a related exponent $η= 1 - χ$ which describes how the average maximal jump sizes in the Order Parameter decays on increasing the system size, is the single exponent that describes the finite-size scaling of a number of distributions related to the fastest growth of the Order Parameter in these problems. Excellent quality scaling analysis are presented for the two single peak distributions corresponding to the Order Parameters at the two ends of the maximal jump, the bimodal distribution constructed by interpolation of these distributions and for the distribution of the maximal jump in the Order Parameter.

cond-mat.stat-mech↗

arXiv2010

A new route to Explosive Percolation

The biased link occupation rule in the Achlioptas process (AP) discourages the large clusters to grow much ahead of others and encourages faster growth of clusters which lag behind. In this paper we propose a model where this tendency is sharply reflected in the Gamma distribution of the cluster sizes, unlike the power law distribution in AP. In this model single edges between pairs of clusters of sizes $s_i$ and $s_j$ are occupied with a probability $\propto (s_is_j)^α$. The parameter $α$ is continuously tunable over the entire real axis. Numerical studies indicate that for $α< α_c$ the transition is first order, $α_c=0$ for square lattice and $α_c=-1/2$ for random graphs. In the limits of $α= -\infty, +\infty$ this model coincides with models well established in the literature.

cond-mat.dis-nn↗

arXiv2009

Weighted Trade Network in a Model of Preferential Bipartite Transactions

Using a model of wealth distribution where traders are characterized by quenched random saving propensities and trade among themselves by bipartite transactions, we mimic the enhanced rates of trading of the rich by introducing the preferential selection rule using a pair of continuously tunable parameters. The bipartite trading defines a growing trade network of traders linked by their mutual trade relationships. With the preferential selection rule this network appears to be highly heterogeneous characterized by the scale-free nodal degree and the link weight distributions and presents signatures of non-trivial strength-degree correlations. With detailed numerical simulations and using finite-size scaling analysis we present evidence that the associated critical exponents are continuous functions of the tuning parameters. However the wealth distribution has been observed to follow the well-known Pareto law robustly for all positive values of the tuning parameters.

q-fin.GN↗

arXiv2009

Branching Process in a Stochastic Extremal Model

We considered a stochastic version of the Bak-Sneppen model (SBSM) of ecological evolution where the the number $M$ of sites mutated in a mutation event is restricted to only two. Here the mutation zone consists of only one site and this site is randomly selected from the neighboring sites at every mutation event in an annealed fashion. The critical behavior of the SBSM is found to be the same as the BS model in dimensions $d$ =1 and 2. However on the scale-free graphs the critical fitness value is non-zero even in the thermodynamic limit but the critical behavior is mean-field like. Finally $ $ has been made even smaller than two by probabilistically updating the mutation zone which also shows the original BS model behavior. We conjecture that a SBSM on any arbitrary graph with any small branching factor greater than unity will lead to a self-organized critical state.

cond-mat.stat-mech↗

arXiv2009

An optimal network for passenger traffic

The optimal solution of an inter-city passenger transport network has been studied using Zipf's law for the city populations and the Gravity law describing the fluxes of inter-city passenger traffic. Assuming a fixed value for the cost of transport per person per kilometer we observe that while the total traffic cost decreases, the total wiring cost increases with the density of links. As a result the total cost to maintain the traffic distribution is optimal at a certain link density which vanishes on increasing the network size. At a finite link density the network is scale-free. Using this model the air-route network of India has been generated and an one-to-one comparison of the nodal degree values with the real network has been made.

physics.soc-ph↗

arXiv2008

The International Trade Network: weighted network analysis and modelling

Tools of the theory of critical phenomena, namely the scaling analysis and universality, are argued to be applicable to large complex web-like network structures. Using a detailed analysis of the real data of the International Trade Network we argue that the scaled link weight distribution has an approximate log-normal distribution which remains robust over a period of 53 years. Another universal feature is observed in the power-law growth of the trade strength with gross domestic product, the exponent being similar for all countries. Using the 'rich-club' coefficient measure of the weighted networks it has been shown that the size of the rich-club controlling half of the world's trade is actually shrinking. While the gravity law is known to describe well the social interactions in the static networks of population migration, international trade, etc, here for the first time we studied a non-conservative dynamical model based on the gravity law which excellently reproduced many empirical features of the ITN.

q-fin.GN↗

arXiv2007

The International Trade Network

Bilateral trade relationships in the international level between pairs of countries in the world give rise to the notion of the International Trade Network (ITN). This network has attracted the attention of network researchers as it serves as an excellent example of the weighted networks, the link weight being defined as a measure of the volume of trade between two countries. In this paper we analyzed the international trade data for 53 years and studied in detail the variations of different network related quantities associated with the ITN. Our observation is that the ITN has also a scale invariant structure like many other real-world networks.

q-fin.GN↗

arXiv2007

A transition from river networks to scale-free networks

A spatial network is constructed on a two dimensional space where the nodes are geometrical points located at randomly distributed positions which are labeled sequentially in increasing order of one of their co-ordinates. Starting with $N$ such points the network is grown by including them one by one according to the serial number into the growing network. The $t$-th point is attached to the $i$-th node of the network using the probability: $π_i(t) \sim k_i(t)\ell_{ti}^α$ where $k_i(t)$ is the degree of the $i$-th node and $\ell_{ti}$ is the Euclidean distance between the points $t$ and $i$. Here $α$ is a continuously tunable parameter and while for $α=0$ one gets the simple Barabási-Albert network, the case for $α\to -\infty$ corresponds to the spatially continuous version of the well known Scheidegger's river network problem. The modulating parameter $α$ is tuned to study the transition between the two different critical behaviors at a specific value $α_c$ which we numerically estimate to be -2.

cond-mat.stat-mech↗

arXiv2006

Self-organized critical earthquake model with moving boundary

A globally driven self-organized critical model of earthquakes with conservative dynamics has been studied. An open but moving boundary condition has been used so that the origin (epicenter) of every avalanche (earthquake) is at the center of the boundary. As a result, all avalanches grow in equivalent conditions and the avalanche size distribution obeys finite size scaling excellent. Though the recurrence time distribution of the time series of avalanche sizes obeys well both the scaling forms recently observed in analysis of the real data of earthquakes, it is found that the scaling function decays only exponentially in contrast to a generalized gamma distribution observed in the real data analysis. The non-conservative version of the model shows periodicity even with open boundary.

cond-mat.stat-mech↗

arXiv2006

Weighted Scale-free Networks in Euclidean Space Using Local Selection Rule

A spatial scale-free network is introduced and studied whose motivation has been originated in the growing Internet as well as the Airport networks. We argue that in these real-world networks a new node necessarily selects one of its neighbouring local nodes for connection and is not controlled by the preferential attachment as in the Barabási-Albert (BA) model. This observation has been mimicked in our model where the nodes pop-up at randomly located positions in the Euclidean space and are connected to one end of the nearest link. In spite of this crucial difference it is observed that the leading behaviour of our network is like the BA model. Defining link weight as an algebraic power of its Euclidean length, the weight distribution and the non-linear dependence of the nodal strength on the degree are analytically calculated. It is claimed that a power law decay of the link weights with time ensures such a non-linear behavior. Switching off the Euclidean space from the same model yields a much simpler definition of the Barabási-Albert model where numerical effort grows linearly with $N$.

cond-mat.stat-mech↗

arXiv2006

Detailed simulation results for some wealth distribution models in Econophysics

In this paper we present detailed simulation results on the wealth distribution model with quenched saving propensities. Unlike other wealth distribution models where the saving propensities are either zero or constant, this model is not found to be ergodic and self-averaging. The wealth distribution statistics with a single realization of quenched disorder is observed to be significantly different in nature from that of the statistics averaged over a large number of independent quenched configurations. The peculiarities in the single realization statistics refuses to vanish irrespective of whatever large sample size is used. This implies that previously observed Pareto law is essentially a convolution of the single member distributions.

physics.soc-ph↗

arXiv2006

Weighted scale-free network with self-organizing link weight dynamics

All crucial features of the recently observed real-world weighted networks are obtained in a model where the weight of a link is defined with a single non-linear parameter $α$ as $w_{ij}=(s_is_j)^α$, $s_i$ and $s_j$ are the strengths of two end nodes of the link and $α$ is a continuously tunable positive parameter. In addition the definition of strength as $s_i= Σ_j w_{ij}$ results a self-organizing link weight dynamics leading to a self-consistent distribution of strengths and weights on the network. Using the Barabási-Albert growth dynamics all exponents of the weighted networks which are continuously tunable with $α$ are obtained. It is conjectured that the weight distribution should be similar in any scale-free network.

cond-mat.stat-mech↗

arXiv2005

Precise toppling balance, quenched disorder, and universality for sandpiles

A single sandpile model with quenched random toppling matrices captures the crucial features of different models of self-organized criticality. With symmetric matrices avalanche statistics falls in the multiscaling BTW universality class. In the asymmetric case the simple scaling of the Manna model is observed. The presence or absence of a precise toppling balance between the amount of sand released by a toppling site and the total quantity the same site receives when all its neighbors topple once determines the appropriate universality class.

cond-mat.stat-mech↗

arXiv2005

Particle-hole symmetry in a sandpile model

In a sandpile model addition of a hole is defined as the removal of a grain from the sandpile. We show that hole avalanches can be defined very similar to particle avalanches. A combined particle-hole sandpile model is then defined where particle avalanches are created with probability $p$ and hole avalanches are created with the probability $1-p$. It is observed that the system is critical with respect to either particle or hole avalanches for all values of $p$ except at the symmetric point of $p_c=1/2$. However at $p_c$ the fluctuating mass density is having non-trivial correlations characterized by $1/f$ type of power spectrum.

cond-mat.stat-mech↗

arXiv2005

Sandpile model on an optimized scale-free network on Euclidean space

Deterministic sandpile models are studied on a cost optimized Barabási-Albert (BA) scale-free network whose nodes are the sites of a square lattice. For the optimized BA network, the sandpile model has the same critical behaviour as the BTW sandpile, whereas for the un-optimized BA network the critical behaviour is mean-field like.

cond-mat.stat-mech↗

arXiv2005

Sandpile model on a quenched substrate generated by kinetic self-avoiding trails

Kinetic self-avoiding trails are introduced and used to generate a substrate of randomly quenched flow vectors. Sandpile model is studied on such a substrate with asymmetric toppling matrices where the precise balance between the net outflow of grains from a toppling site and the total inflow of grains to the same site when all its neighbors topple once is maintained at all sites. Within numerical accuracy this model behaves in the same way as the multiscaling BTW model.

cond-mat.stat-mech↗