arXiv subjects

Arnab Chatterjee

Publications and source records attributed to Arnab Chatterjee.

At least 55 records · Page 3Linked to original sources

arXiv2015

Social inequality: from data to statistical physics modeling

Social inequality is a topic of interest since ages, and has attracted researchers across disciplines to ponder over it origin, manifestation, characteristics, consequences, and finally, the question of how to cope with it. It is manifested across different strata of human existence, and is quantified in several ways. In this review we discuss the origins of social inequality, the historical and commonly used non-entropic measures such as Lorenz curve, Gini index and the recently introduced $k$ index. We also discuss some analytical tools that aid in understanding and characterizing them. Finally, we argue how statistical physics modeling helps in reproducing the results and interpreting them.

physics.soc-ph↗

arXiv2014

Socio-economic inequalities: a statistical physics perspective

Socio-economic inequalities are manifested in different aspects of our social life. We discuss various aspects, beginning with the evolutionary and historical origins, and discussing the major issues from the social and economic point of view. The subject has attracted scholars from across various disciplines, including physicists, who bring in a unique perspective to the field. The major attempts to analyze the results, address the causes, and understand the origins using statistical tools and statistical physics concepts are discussed.

physics.soc-ph↗

arXiv2014

Zipf's law in city size from a resource utilization model

We study a resource utilization scenario characterized by intrinsic fitness. To describe the growth and organization of different cities, we consider a model for resource utilization where many restaurants compete, as in a game, to attract customers using an iterative learning process. Results for the case of restaurants with uniform fitness are reported. When fitness is uniformly distributed, it gives rise to a Zipf law for the number of customers. We perform an exact calculation for the utilization fraction for the case when choices are made independent of fitness. A variant of the model is also introduced where the fitness can be treated as an ability to stay in the business. When a restaurant loses customers, its fitness is replaced by a random fitness. The steady state fitness distribution is characterized by a power law, while the distribution of the number of customers still follows the Zipf law, implying the robustness of the model. Our model serves as a paradigm for the emergence of Zipf law in city size distribution.

physics.soc-ph↗

arXiv2014

Statistical Mechanics of Competitive Resource Allocation using Agent-based Models

Demand outstrips available resources in most situations, which gives rise to competition, interaction and learning. In this article, we review a broad spectrum of multi-agent models of competition (El Farol Bar problem, Minority Game, Kolkata Paise Restaurant problem, Stable marriage problem, Parking space problem and others) and the methods used to understand them analytically. We emphasize the power of concepts and tools from statistical mechanics to understand and explain fully collective phenomena such as phase transitions and long memory, and the mapping between agent heterogeneity and physical disorder. As these methods can be applied to any large-scale model of competitive resource allocation made up of heterogeneous adaptive agent with non-linear interaction, they provide a prospective unifying paradigm for many scientific disciplines.

physics.soc-ph↗

arXiv2014

Measuring social inequality with quantitative methodology: analytical estimates and empirical data analysis by Gini and $k$ indices

Social inequality manifested across different strata of human existence can be quantified in several ways. Here we compute non-entropic measures of inequality such as Lorenz curve, Gini index and the recently introduced $k$ index analytically from known distribution functions. We characterize the distribution functions of different quantities such as votes, journal citations, city size, etc. with suitable fits, compute their inequality measures and compare with the analytical results. A single analytic function is often not sufficient to fit the entire range of the probability distribution of the empirical data, and fit better to two distinct functions with a single crossover point. Here we provide general formulas to calculate these inequality measures for the above cases. We attempt to specify the crossover point by minimizing the gap between empirical and analytical evaluations of measures. Regarding the $k$ index as an `extra dimension', both the lower and upper bounds of the Gini index are obtained as a function of the $k$ index. This type of inequality relations among inequality indices might help us to check the validity of empirical and analytical evaluations of those indices.

physics.soc-ph↗

arXiv2014

The Nobel Prize delay

The time lag between the publication of a Nobel discovery and the conferment of the prize has been rapidly increasing for all disciplines, especially for Physics. Does this mean that fundamental science is running out of groundbreaking discoveries?

physics.soc-ph↗

arXiv2014

On the evolution and utility of annual citation indices

We study the statistics of citations made to the top ranked indexed journals for Science and Social Science databases in the Journal Citation Reports using different measures. Total annual citation and impact factor, as well as a third measure called the annual citation rate are used to make the detailed analysis. We observe that the distribution of the annual citation rate has an universal feature - it shows a maximum at the rate scaled by half the average, irrespective of how the journals are ranked, and even across Science and Social Science journals, and fits well to log-Gumbel distribution. Correlations between different quantities are studied and a comparative analysis of the three measures is presented. The newly introduced annual citation rate factor helps in understanding the effect of scaling the number of citation by the total number of publications. The effect of the impact factor on authors contributing to the journals as well as on editorial policies is also discussed.

cs.DL↗

arXiv2013

Universality in voting behavior: an empirical analysis

Election data represent a precious source of information to study human behavior at a large scale. In proportional elections with open lists, the number of votes received by a candidate, rescaled by the average performance of all competitors in the same party list, has the same distribution regardless of the country and the year of the election. Here we provide the first thorough assessment of this claim. We analyzed election datasets of 15 countries with proportional systems. We confirm that a class of nations with similar election rules fulfill the universality claim. Discrepancies from this trend in other countries with open-lists elections are always associated with peculiar differences in the election rules, which matter more than differences between countries and historical periods. Our analysis shows that the role of parties in the electoral performance of candidates is crucial: alternative scalings not taking into account party affiliations lead to poor results.

physics.soc-ph↗

arXiv2012

Continuous transition of social efficiencies in the stochastic strategy Minority Game

We show that in a variant of the Minority Game problem, the agents can reach a state of maximum social efficiency, where the fluctuation between the two choices is minimum, by following a simple stochastic strategy. By imagining a social scenario where the agents can only guess about the number of excess people in the majority, we show that as long as the guess value is sufficiently close to the reality, the system can reach a state of full efficiency or minimum fluctuation. A continuous transition to less efficient condition is observed when the guess value becomes worse. Hence, people can optimize their guess value for excess population to optimize the period of being in the majority state. We also consider the situation where a finite fraction of agents always decide completely randomly (random trader) as opposed to the rest of the population that follow a certain strategy (chartist). For a single random trader the system becomes fully efficient with majority-minority crossover occurring every two-days interval on average. For just two random traders, all the agents have equal gain with arbitrarily small fluctuations.

physics.soc-ph↗

arXiv2012

Disorder induced phase transition in kinetic models of opinion dynamics

We propose a model of continuous opinion dynamics, where mutual interactions can be both positive and negative. Different types of distributions for the interactions, all characterized by a single parameter $p$ denoting the fraction of negative interactions, are considered. Results from exact calculation of a discrete version and numerical simulations of the continuous version of the model indicate the existence of a universal continuous phase transition at p=p_c below which a consensus is reached. Although the order-disorder transition is analogous to a ferromagnetic-paramagnetic phase transition with comparable critical exponents, the model is characterized by some distinctive features relevant to a social system.

physics.soc-ph↗

arXiv2012

Phase transitions in crowd dynamics of resource allocation

We define and study a class of resources allocation processes where $gN$ agents, by repeatedly visiting $N$ resources, try to converge to optimal configuration where each resource is occupied by at most one agent. The process exhibits a phase transition, as the density $g$ of agents grows, from an absorbing to an active phase. In the latter, even if the number of resources is in principle enough for all agents ($g<1$), the system never settles to a frozen configuration. We recast these processes in terms of zero-range interacting particles, studying analytically the mean field dynamics and investigating numerically the phase transition in finite dimensions. We find a good agreement with the critical exponents of the stochastic fixed-energy sandpile. The lack of coordination in the active phase also leads to a non-trivial faster-is-slower effect.

physics.soc-ph↗

arXiv2011

Antipersistent dynamics in kinetic models of wealth exchange

We investigate the detailed dynamics of gains and losses made by agents in some kinetic models of wealth exchange. The concept of a walk in an abstract gain-loss space for the agents had been introduced in an earlier work. For models in which agents do not save, or save with uniform saving propensity, this walk has diffusive behavior. In case the saving propensity $λ$ is distributed randomly ($0 \leq λ< 1$), the resultant walk showed a ballistic nature (except at a particular value of $λ^* \approx 0.47$). Here we consider several other features of the walk with random $λ$. While some macroscopic properties of this walk are comparable to a biased random walk, at microscopic level, there are gross differences. The difference turns out to be due to an antipersistent tendency towards making a gain (loss) immediately after making a loss (gain). This correlation is in fact present in kinetic models without saving or with uniform saving as well, such that the corresponding walks are not identical to ordinary random walks. In the distributed saving case, antipersistence occurs with a simultaneous overall bias.

physics.soc-ph↗

arXiv2011

Phase transitions and non-equilibrium relaxation in kinetic models of opinion formation

We review in details some recently proposed kinetic models of opinion dynamics. We discuss the several variants including a generalised model. We provide mean field estimates for the critical points, which are numerically supported with reasonable accuracy. Using non-equilibrium relaxation techniques, we also investigate the nature of phase transitions observed in these models. We study the nature of correlations as the critical points are approached, and comment on the universality of the phase transitions observed.

physics.soc-ph↗

arXiv2010

Agent dynamics in kinetic models of wealth exchange

We study the dynamics of individual agents in some kinetic models of wealth exchange, particularly, the models with savings. For the model with uniform savings, agents perform simple random walks in the "wealth space". On the other hand, we observe ballistic diffusion in the model with distributed savings. There is an associated skewness in the gain-loss distribution which explains the steady state behavior in such models. We find that in general an agent gains while interacting with an agent with a larger saving propensity.

physics.soc-ph↗

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↗

arXiv2010

Statistics of the Kolkata Paise Restaurant Problem

We study the dynamics of a few stochastic learning strategies for the 'Kolkata Paise Restaurant' problem, where N agents choose among N equally priced but differently ranked restaurants every evening such that each agent tries get to dinner in the best restaurant (each serving only one customer and the rest arriving there going without dinner that evening). We consider the learning strategies to be similar for all the agents and assume that each follow the same probabilistic or stochastic strategy dependent on the information of the past successes in the game. We show that some 'naive' strategies lead to much better utilization of the services than some relatively 'smarter' strategies. We also show that the service utilization fraction as high as 0.80 can result for a stochastic strategy, where each agent sticks to his past choice (independent of success achieved or not; with probability decreasing inversely in the past crowd size). The numerical results for utilization fraction of the services in some limiting cases are analytically examined.

physics.soc-ph↗

arXiv2009

The Kolkata Paise Restaurant Problem and Resource Utilization

We study the dynamics of the "Kolkata Paise Restaurant problem". The problem is the following: In each period, N agents have to choose between N restaurants. Agents have a common ranking of the restaurants. Restaurants can only serve one customer. When more than one customer arrives at the same restaurant, one customer is chosen at random and is served; the others do not get the service. We first introduce the one-shot versions of the Kolkata Paise Restaurant problem which we call one-shot KPR games. We then study the dynamics of the Kolkata Paise Restaurant problem (which is a repeated game version of any given one shot KPR game) for large N. For statistical analysis, we explore the long time steady state behavior. In many such models with myopic agents we get under-utilization of resources, that is, we get a lower aggregate payoff compared to the social optimum. We study a number of myopic strategies, focusing on the average occupation fraction of restaurants.

physics.soc-ph↗

arXiv2009

Kinetic models for wealth exchange on directed networks

We propose some kinetic models of wealth exchange and investigate their behavior on directed networks though numerical simulations. We observe that network topology and directedness yields a variety of interesting features in these models. The nature of asset distribution in such directed networks show varied results, the degree of asset inequality increased with the degree of disorder in the graphs.

physics.soc-ph↗