arXiv subjects

Bikas K. Chakrabarti

Publications and source records attributed to Bikas K. Chakrabarti.

At least 37 records · Page 2Linked to original sources

arXiv2023

Scaling and Kinetic Exchange Like Behavior of Hirsch Index and Total Citation Distributions: Scopus-CiteScore Data Analysis

We analyze the data distributions $f(h)$, $f(N_c$) and $f(N_p)$ of the Hirsch index $(h)$, total citations ($N_c$) and total number of papers ($N_p$) of the top scoring 120,000 authors (scientists) from the Stanford cite-score (or c-score) 2022 list and their corresponding $h$ ($3 \le h \le 284$), $N_c (1009 \le N_c \le 428620$) and $N_p$ ($3\le N_p \le 3791$) statistics from the Scopus data. For reasons explained in the text, we divided the data of these top scorers (c-scores in the range 5.6125 to 3.3461) into six successive equal-sized Groups of 20,000 authors or scientists. We tried to fit, in each Group, $f(h)$, $f(Nc)$ and $f(Np)$ with Gamma distributions, viewing them as the ``wealth distributions'' in the fixed saving-propensity kinetic exchange models and found $f(h) \sim h^{γ_h} \mathrm{exp} (-h/T_h)$ with fitting noise level or temperature level ($T_h$) and average value of $h$, and the power $γ_h$ determined by the ``citation saving propensity'' in each Group. We further showed that using some earlier proposed power law scaling like $h = D_c N_c^{α_c}$ (or $h = D_p N_p^{α_p}$) with $α_c = 1/2 = α_p$, we can derive the observed $f(h)$ from the observed $f(N_c)$ or $f(N_p)$, with $D_c = 0.5$, but $D_p$ depending on the Group considered. This observation suggests that the average citations per paper ($N_c/N_p$) in each group ($= (D_p/D_c)^2 =4D_p^2$) vary (from 58 to 29) with the c-score range of the six Groups considered here, implying different effective Dunbar-like coordination numbers of the scientists belonging to different groups or networks.

physics.soc-ph↗

arXiv2023

Inequality of avalanche sizes in models of fracture

Prediction of an imminent catastrophic event in a driven disordered system is of paramount importance - from the laboratory scale controlled fracture experiment to the largest scale of mechanical failure i.e., earthquakes. It has been long conjectured that the statistical regularities in the energy emission time series mirrors the "health" of such driven systems and hence have the potential for forecasting imminent catastrophe. Among other statistical regularities, a measure of how unequal the avalanche sizes are, is potentially a crucial indicator of imminent failure. The inequalities of avalanche sizes are quantified using inequality indices traditionally used in socio-economic systems: the Gini index (g), the Hirsch index (h) and the Kolkata index (k). It is then shown analytically (for mean field) and numerically (for non mean field) in models of quasi-brittle materials that the indices show universal behavior near the breaking points in such models and hence could serve as indicators of imminent breakdown of stressed disordered systems.

cond-mat.stat-mech↗

arXiv2023

Social dynamics through kinetic exchange: The BChS model

This review presents an overview of the current research in kinetic exchange models for opinion formation in a society. The review begins with a brief introduction to previous models and subsequently provides an in-depth discussion of the progress achieved in the Biswas-Chatterjee-Sen model proposed in 2012, also known as the BChS model in some later research publications. The unique feature of the model is its inclusion of negative interaction between agents. The review covers various topics, including phase transitions between different opinion states, critical behavior dependent on various parameters, and applications in realistic scenarios such as the United States presidential election and Brexit.

physics.soc-ph↗

arXiv2023

Sandpile Universality in Social Inequality: Gini and Kolkata Measures

Social inequalities are ubiquitous and evolve towards a universal limit. Herein, we extensively review the values of inequality measures, namely the Gini ($g$) index and the Kolkata ($k$) index, two standard measures of inequality used in the analysis of various social sectors through data analysis. The Kolkata index, denoted as $k$, indicates the proportion of the `wealth' owned by $(1-k)$ fraction of the `people'. Our findings suggest that both the Gini index and the Kolkata index tend to converge to similar values (around $g=k \approx 0.87$, starting from the point of perfect equality, where $g=0$ and $k=0.5$) as competition increases in different social institutions, such as markets, movies, elections, universities, prize winning, battle fields, sports (Olympics), etc., under conditions of unrestricted competition (no social welfare or support mechanism). In this review, we present the concept of a generalized form of Pareto's 80/20 law ($k=0.80$), where the coincidence of inequality indices is observed. The observation of this coincidence is consistent with the precursor values of the $g$ and $k$ indices for the self-organized critical (SOC) state in self-tuned physical systems such as sand piles. These results provide quantitative support for the view that interacting socioeconomic systems can be understood within the framework of SOC, which has been hypothesized for many years. These findings suggest that the SOC model can be extended to capture the dynamics of complex socioeconomic systems and help us better understand their behavior.

physics.soc-ph↗

arXiv2023

Quantum Annealing: An Overview

In this review, after providing the basic physical concept behind quantum annealing (or adiabatic quantum computation), we present an overview of some recent theoretical as well as experimental developments pointing to the issues which are still debated. With a brief discussion on the fundamental ideas of continuous and discontinuous quantum phase transitions, we discuss the Kibble-Zurek scaling of defect generation following a ramping of a quantum many body system across a quantum critical point. In the process, we discuss associated models, both pure and disordered, and shed light on implementations and some recent applications of the quantum annealing protocols. Furthermore, we discuss the effect of environmental coupling on quantum annealing. Some possible ways to speed up the annealing protocol in closed systems are elaborated upon: We especially focus on the recipes to avoid discontinuous quantum phase transitions occurring in some models where energy gaps vanish exponentially with the system size.

cond-mat.stat-mech↗

arXiv2022

Scaling Behavior of the Hirsch Index for Failure Avalanches, Percolation Clusters and Paper Citations

A popular measure for citation inequalities of individual scientists has been the Hirsch index ($h$). If for any scientist the number $n_c$ of citations is plotted against the serial number $n_p$ of the paper having those many citations (when the papers are ordered from highest cited to lowest) then $h$ corresponds to the nearest lower integer value of $n_p$ below the fixed point of the non-linear citation function (or given by $n_c = h = n_p$ if both $n_p$ and $n_c$ are dense set of integers near the $h$ value). The same index can be estimated (from $h=s=n_{s}$) for the avalanche or cluster of size ($s$) distributions ($n_s$) in elastic fiber bundle or percolation models. Another such inequality index, called the Kolkata index ($k$) says that $(1-k)$ fraction of papers attract $k$ fraction of citations ($k=0.80$ corresponds to the 80-20 law of Pareto). We find, for stress ($σ$), lattice occupation probability ($p$) or Kolkata index ($k$) near the bundle failure threshold ($σ_c$) or percolation threshold ($p_c$) or critical value of Kolkata index $k_c$, good fit to Widom-Stauffer like scaling $h/[\sqrt{N}/log N]$ = $f(\sqrt{N}[σ_c -σ]^α)$, $h/[\sqrt{N}/log N]=f(\sqrt{N}|p_c -p|^α)$ or $h/[\sqrt{N_c}/log N_c]=f(\sqrt{N_c}|k_c -k|^α)$ respectively, with asymptotically defined scaling function $f$, for systems of size $N$ (total number of fibers or lattice sites) or $N_c$ (total number of citations), and $α$ denoting the appropriate scaling exponent. We also show that if the number ($N_m$) of members of parliaments or national assemblies of different countries (with population $N$) is identified as their respective $h-$index, then the data fit the scaling relation $N_m \sim \sqrt N /log N$, resolving a major recent controversy.

physics.soc-ph↗

arXiv2022

Evolutionary Dynamics of Social Inequality and Coincidence of Gini and Kolkata indices under Unrestricted Competition

Social inequalities are ubiquitous and here we show that the values of the Gini ($g$) and Kolkata ($k$) indices, two generic inequality indices, approach each other (starting from $g = 0$ and $k = 0.5$ for equality) as the competitions grow in various social institutions like markets, universities, elections, etc. It is further showed that these two indices become equal and stabilize at a value (at $g = k \simeq 0.87$) under unrestricted competitions. We propose to view this coincidence of inequality indices as a generalized version of the (more than a) century old 80-20 law of Pareto. Furthermore, the coincidence of the inequality indices noted here is very similar to the ones seen before for self-organized critical (SOC) systems. The observations here, therefore, stand as a quantitative support towards viewing interacting socio-economic systems in the framework of SOC, an idea conjectured for years.

physics.soc-ph↗

arXiv2022

Success of Social Inequality Measures in Predicting Critical or Failure Points in Some Models of Physical Systems

Statistical physicists and social scientists both study extensively some characteristic features of the unequal distributions of energy, cluster or avalanche sizes and of income, wealth etc among the particles (or sites) and population respectively. While physicists concentrate on the self-similar (fractal) structure (and the characteristic exponents) of the largest (percolating) cluster or avalanche, social scientists study the inequality indices like Gini and Kolkata etc given by the non-linearity of the Lorenz function representing the cumulative fraction of the wealth possessed by different fraction of the population. We review here, using results from earlier publications and some new numerical as well as analytical results, how the above-mentioned social inequality indices, when extracted from the unequal distributions of energy (in kinetic exchange models), cluster sizes (in percolation models) or avalanche sizes (in self-organized critical or fiber bundle models) can help in a major way in providing precursor signals for an approaching critical point or imminent failure point. Extensive numerical and some analytical results have been discussed.

physics.soc-ph↗

arXiv2022

Near universal values of social inequality indices in self-organized critical models

We have studied few social inequality measures associated with the sub-critical dynamical features (measured in terms of the avalanche size distributions) of four self-organized critical models while the corresponding systems approach their respective stationary critical states. It has been observed that these inequality measures (specifically the Gini and Kolkata indices) exhibit nearly universal values though the models studied here are widely different, namely the Bak-Tang-Wiesenfeld sandpile, the Manna sandpile and the quenched Edwards-Wilkinson interface, and the fiber bundle interface. These observations suggest that the self-organized critical systems have broad similarity in terms of these inequality measures. A comparison with similar earlier observations in the data of socio-economic systems with unrestricted competitions suggest the emergent inequality as a result of the possible proximity to the self-organized critical states.

cond-mat.stat-mech↗

arXiv2022

Variation of Gini and Kolkata Indices with Saving Propensity in the Kinetic Exchange Model of Wealth Distribution: An Analytical Study

We study analytically the change in the wealth ($x$) distribution $P(x)$ against saving propensity $λ$ in a closed economy, using the Kinetic theory. We estimate the Gini ($g$) and Kolkata ($k)$ indices by deriving (using $P(x)$) the Lorenz function $L(f)$, giving the cumulative fraction $L$ of wealth possessed by fraction $f$ of the people ordered in ascending order of wealth. First, using the exact result for $P(x)$ when $λ= 0$ we derive $L(f)$, and from there the index values $g$ and $k$. We then proceed with an approximate gamma distribution form of $P(x)$ for non-zero values of $λ$. Then we derive the results for $g$ and $k$ at $λ= 0.25$ and as $λ\rightarrow 1$. We note that for $λ\rightarrow 1$ the wealth distribution $P(x)$ becomes a Dirac $δ$-function. Using this and assuming that form for larger values of $λ$ we proceed for an approximate estimate for $P(x)$ centered around the most probable wealth (a function of $λ$). We utilize this approximate form to evaluate $L(f)$, and using this along with the known analytical expression for $g$, we derive an analytical expression for $k(λ)$. These analytical results for $g$ and $k$ at different $λ$ are compared with numerical (Monte Carlo) results from the study of the Chakraborti-Chakrabarti model. Next we derive analytically a relation between $g$ and $k$. From the analytical expressions of $g$ and $k$, we proceed for a thermodynamic mapping to show that the former corresponds to entropy and the latter corresponds to the inverse temperature.

physics.soc-ph↗

arXiv2021

Kinetic Exchange Income Distribution Models with Saving Propensities: Inequality Indices and Self-Organised Poverty Level

We report the numerical results for the steady state income or wealth distribution $P(m)$ and the resulting inequality measures (Gini $g$ and Kolkata $k$ indices) in the kinetic exchange models of market dynamics. We study the variations of $P(m)$ and of the indices $g$ and $k$ with the saving propensity $λ$ of the agents, with two different kinds of trade (kinetic exchange) dynamics. In the first case, the exchange occurs between randomly chosen pairs of agents and in the next, one of the agents in the chosen pair is the poorest of all and the other agent is randomly picked up from the rest of the population (where, in the steady state, a self-organized poverty level or SOPL appears). These studies have also been made for two different kinds of saving behaviors. One, where each agent has the same value of $λ$ (constant over time) and the other where $λ$ for each agent can take two values (0 and 1), changing randomly over a fraction of time $ρ(<1)$ of choosing $λ= 1$. We find that the inequality decreases with increasing savings ($λ$); inequality indices ($g$ and $k$) decrease and SOPL increases with increasing $λ$, indicating possible applications in economic policy making.

physics.soc-ph↗

arXiv2021

Social Inequality Analysis of Fiber Bundle Model Statistics and Prediction of Materials Failure

Inequalities are abundant in a society with a number of agents competing for a limited amount of resource. Statistics of such social inequalities are usually represented by the Lorenz function $L(p)$, where $p$ fraction of the population possesses $L(p)$ fraction of the total wealth, when the population is arranged in the ascending order of their wealth. Similarly, in scientometrics, such inequalities can be represented by a plot of the citation count against the respective number of papers by a scientist, again arranged in the ascending order of their citation counts. Quantitatively, these inequalities are captured by the corresponding inequality indices, namely the Kolkata $k$ and the Hirsch $h$ indices, given by the fixed points of these nonlinear functions. In statistical physics of criticality, the fixed points of the Renormalization Group generator functions are studied in their self-similar limit, where its (fractal) structure converges to a unique form. The statistical indices in the social science, however, correspond to the fixed points where the values of the generator function (wealth or citation sizes) are commensurately abundant in fractions or numbers (of persons or papers). We introduce and study these indices for the inequalities of (pre-failure) avalanches, given by their size distributions in the Fiber Bundle Models (FBM) of non-brittle materials. We show how a prior knowledge of the terminal and almost universal value of the $k$ index for a wide range of disorder parameter, can help in predicting an imminent catastrophic breakdown in the model. This observation has also been complemented by noting a similar (but not identical) behavior of the Hirsch index ($h$), redefined for such avalanche statistics.

cond-mat.stat-mech↗

arXiv2020

Cooperative dynamics in the Fiber Bundle Model

We discuss the cooperative failure dynamics in the Fiber Bundle Model where the individual elements or fibers are Hookean springs, having identical spring constant but different breaking strengths. When the bundle is stressed or strained, especially in the equal-load-sharing scheme, the load supported by the failed fiber gets shared equally by the rest of the surviving fibers. This mean-field type statistical feature (absence of fluctuations) in the load-sharing mechanism helped major analytical developments in the study of breaking dynamics in the model and precise comparisons with simulation results. We intend to present a brief review on these developments.

cond-mat.stat-mech↗

arXiv2020

The Ising universality class of kinetic exchange models of opinion dynamics

We show using scaling arguments and Monte Carlo simulations that a class of binary interacting models of opinion evolution belong to the Ising universality class in presence of an annealed noise term of finite amplitude. While the zero noise limit is known to show an active-absorbing transition, addition of annealed noise induces a continuous order-disorder transition with Ising universality class in the infinite-range (mean field) limit of the models.

physics.soc-ph↗

arXiv2020

Inequality Measures: The Kolkata index in comparison with other measures

We provide a survey of the Kolkata index of social inequality, focusing in particular on income inequality. Based on the observation that inequality functions (such as the Lorenz function), giving the measures of income or wealth against that of the population, to be generally nonlinear, we show that the fixed point (like Kolkata index k) of such a nonlinear function (or related, like the complementary Lorenz function) offer better measure of inequality than the average quantities (like Gini index). Indeed the Kolkata index can be viewed as a generalized Hirsch index for a normalized inequality function and gives the fraction k of the total wealth possessed by the rich (1-k) fraction of the population. We analyze the structures of the inequality indices for both continuous and discrete income distributions. We also compare the Kolkata index to some other measures like the Gini coefficient and the Pietra index. Lastly, we provide some empirical studies which illustrate the differences between the Kolkata index and the Gini coefficient.

econ.GN↗

arXiv2020

Phase transition in the Kolkata Paise Restaurant problem

A novel phase transition behaviour is observed in the Kolkata Paise Restaurant (KPR) problem where large number ($N$) of agents or customers collectively (and iteratively) learn to choose among the $N$ restaurants where she would expect to be alone that evening and would get the only dish available there (or may get randomly picked up if more than one agent arrive there that evening). The players are expected to evolve their strategy such that the publicly available information about past crowd in different restaurants can be utilized and each of them is able to make the best minority choice. For equally ranked restaurants we follow two crowd-avoiding strategies: Strategy I, where each of the $n_i(t)$ number of agents arriving at the $i$-th restaurant on the $t$-th evening goes back to the same restaurant on the next evening with probability $[n_i(t)]^{-α}$, while in Strategy II, with probability $p$, when $n_i(t) > 1$. We study the steady state ($t$-independent) utilization fraction $f:(1-f)$ giving the steady state (wastage) fraction of restaurants going without any customer in any particular evening. With both the strategies we find, near $α_c=0_+$ (in strategy I) or $p=1_-$ (in strategy II), the steady state wastage fraction $(1-f)\propto(α- α_c)^β$ or $(p_c - p)^β$ with $β\simeq 0.8, 0.87, 1.0$ and the convergence time $τ$ (for $f(t)$ becoming independent of $t$) varies as $τ\propto{(α-α_c)}^{-γ}$ or ${(p_c-p)}^{-γ}$, with $γ\simeq 1.18, 1.11, 1.05$ in infinite-dimension (rest of the $N-1$ neighboring restaurants), three-dimension ($6$ neighbors) and two-dimension ($4$ neighbors) respectively.

physics.soc-ph↗

arXiv2020

Flory-like Statistics of Fracture in Fiber Bundle Model as obtained via Kolmogorov Dispersion for Turbulence: A conjecture

It has long been conjectured that (rapid) fracture propagation dynamics in materials and turbulent motion of fluids are two manifestations of the same physical process. The universality class of turbulence (Kolmogorov dispersion in particular) had been conjectured to be identifiable with the Flory statistics for linear polymers (self-avoiding walks on lattices). These help us to relate fracture statistics to those of linear polymers (Flory statistics). The statistics of fracture in the Fiber Bundle Model (FBM) are now well studied and many exact results are now available for the equal load-sharing (ELS) scheme. Yet, the correlation length exponent in this model was missing and we show here how the correspondence between fracture statistics and the Flory mapping of Kolmogorov statistics for turbulence helps us to make a conjecture about the value of the correlation length exponent for fracture in the ELS limit of FBM, and also about the upper critical dimension. Besides, the fracture avalanche size exponent values in lower dimensions (as estimated from such mapping to Flory statistics) also compare well with the observations.

cond-mat.stat-mech↗

arXiv2019

On the Kolkata index as a measure of income inequality

We study the mathematical and economic structure of the Kolkata (k) index of income inequality. We show that the k-index always exists and is a unique fixed point of the complementary Lorenz function, where the Lorenz function itself gives the fraction of cumulative income possessed by the cumulative fraction of population (when arranged from poorer to richer). We show that the k-index generalizes Pareto's 80/20 rule. Although the k and Pietra indices both split the society into two groups, we show that k-index is a more intensive measure for the poor-rich split. We compare the normalized k-index with the Gini coefficient and the Pietra index and discuss when they coincide. We establish that for any income distribution the value of Gini coefficient is no less than that of the Pietra index and the value of the Pietra index is no less than that of the normalized k-index. While the Gini coefficient and the Pietra index are affected by transfers exclusively among the rich or among the poor, the k-index is only affected by transfers across the two groups.

econ.TH↗